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Adiabatic atmospheric boundary layers a review and analysis of data from the period 1880-1972



Central Electricit!, Research Laboratories, Learhsrhead. Surrey IX1 ‘SE

Many inconsistencies are ShoWI to have rxisttd in earlier prssent3rions and r2uiews. particutaric with respect to quantifying the power indices and turbuiencs intensities ~pprupriarto row&er terrains. and the variation of ths WbthGe length scales with height and Wrain type- These are resolved by defining from the data four distinct terrain types. The variation of the pour index. tu~bLllencc intensity and Reynolds stresses with thee terrain types is shown 10 fol10~ the Qrne law. It is also shown thal the longitudinal length scale of rurbuience decreases uirh increase OCterrain roughness: a simple law is also propound for its variation with both hrighr and xrrain ttx.

constant in Iongitudinal turbulsnce eqtration c5nstant _in veiocity profie tog-law constant in larerai turbuience equation constant in velocity profile log-law constant in vertical turbtilcnee rquatiarr drag cocficient. 2 Ejii: consfant in velocity profile. linear taw zero-plane displacement. m Coriolis parameter. s- L normalised power spectral function s- ’ non-ditiensionat frequency, nr;7i non-dimensional frequency corresponding to peak 11S(n) or II f,,(flI roughness height. m wave number. 2 xrr%Xm-’ Wave number corresponding to peak at‘ nS{n),m .. C Van Karman’s constant constant in Davenport and Harris power spectra eyuations. m longitudinal turbulence length scales. m [Lu, derived Cram autocorrefatron or spectrai date: Gt, and Ltr, are Eulerian isngth scales] vertica1 turbuience length scale. m frequency. s- ’ correlation coefficient auto-correlation coefficient separation distance. m ~CXWX spectral density at freqtrcnc:v in), m”$-’


denotes a iiucIuating contribudon.

power cospecrwl densit]: at frequencr (nf. mJs-I free-stream or gradient friction vclocit~, \, : p
velocity m S-I

the cotfapw of thr Ferrybridge cooling tovzers in 1965 a wind tunnel programme was initiated at C.E,R,L. p3xitral Electricity Research Laboratoriesf to investigate ths stresscts in model cooling towers arising from mean and punctuating wind loads. The highest wind loads occur in the strong winds in which the efkct of buognccy forces is small and mecIxGc&~y produced ~u~~~~enc~ ~~edorn~n~~e~. Thsretbre. in order that mod4 loads should be representative of fuli-scale loads. it is essential that such tests should tx carried out in a tk~ which is a realistic model of an adiabatic boundary layer.


* This review is based orx Part I of thesis submittrd for degree of Ph.D.. the City University. London {March i97-t)‘

The pro&m of simuiaring the boundary layer Row over rural terrain, where most power stations are sit&. was considered first. For this case there existed




up-to-date full scale data from which the general properties of rural boundary labers could be deduced. and on which the subsequent simulation was modelled. The problem of detining a typical urban boundary laysr was morr: diticult since the available data appearsd to be sparse and uncorrelated. in addition. the literature showed that various anomalies existed. both in published data and their analyses. with respect to most terrain types. Many of these anomalies could be attributed to the following. (a) Truly adiabatic conditions are infrequently completely established. (b) If such conditions are established initially, they may change during any test when data are being recorded. (c) Lack of suficient fetch to establish true boundary layer equilibrium. Therefore. a thorough review and analysis of the available literature was undertaken. with the object of producing a consistent picture of the structure of adiabatic boundary layers. In the revisvv some effort has been made to avoid inconsistencies arising from the above. and other factors. by using the following procedures. The data considered were those which were specified as applying to adiabatic or near-adiabatic conditions. When such conditions were not specified. or temperature profiles were not measured, then only data for wind speeds in excess of Sm 5-l. at z = IOm. were considered. M’hsre details of the test site fetch were not given. it was assumed that an adequate fetch was one of the f;tctors taken into account when choosing the site. It was also considered that an assessment of all the relevant data. would help to isolate any that were invalid. In addition. it was intended to present all the data as a function of the roughness length for simplicity of application and to bring some order to the subject. This is not in complete agreement with theoretical treatments which require some data presented as a function of the Rossby number. However. vartations in the Rossby number in strong winds are almost entirely due to variations in the roughness length. 1. .ADIAB.ATIC

various aspects of the boundary formulas.

layer by empirical

2. I. 1 Prrioti ISY@l959. Early ideas on the structure of the flow near the Earth’s surface u'srz derived from observations of cloud and particle movements. Rawson (1913) commented on the presence of motions which could be described as non-periodic or turbulent. These motions decreased in intensity with increase of height. Shaw (191-t) showed how the character of turbulence changed as it encountered large obstructions and illustrated its degree of randomness. Taylor (1915) attempted to describe this tlow theoretically by considering the “average” effect of a collection of eddies rather than the complex mathematical problem of individual eddies. Richardson (1920) showed that the “kinetic energy of eddying’* vvas extracted from the mean wind by the work done by the eddy stresses on the rate of mean strain; this can be defined as the rate at which the mean wind gives LIP energy to these eddies in the production of turbulence. The analysis of turbulence by statistical methods was later expanded by Taylor (1921) who introduced the concept of describing the Row structure by correlation measurements.

In the following text. each of the more important boundary layer quantities is considered separately. In this way. the gradual accumulation of knowledge on the various quantities can be described in chronological order. Some of the main advances in quantifying the properties of adiabatic boundary layers were made in the period IdSO--1959. Therefore. the treatment of that period vviill be more detailed than that of the more recent literature. The subsequent period. from I9hCr1973. is noteworthy for the accumulation of a considerable amount of measurements from various sites and for attempts by many authors (e.g. Davenport. Harris. Panofsky and Pasquill) to describe

where .Yis the distance traversed by a particle in time 7: This reduced the problem of turbulent diffusion to the consideration of one quantity. namely the Lagrangian correlation coefficient R<. which is also relevant to the study of the structure of turbulence. Observations by Goldie (193) showed that the air near the ground consisted of partially formed. rapidly disintegrating eddies. It was initially thought that the eddy velocities were isotropic. Becker (19301. Sherlock and Stout (1932) and Giblett (1932) investigated the validity of this concept. Giblett. in demonstrating the random motion of the air. also showed that its structure was dependent on the state of atmospheric thermal stratification. Durst deduced from Giblett’s data that the shear in the flow resulted in the formation of -‘rolled-up” eddies with their axes across the stream. Best (1935) demonstrated that the longitudinal. lateral and vertical eddy velocities were not the same in magnitude; he also showed that the flow consisted of eddies of various sizes. The production of turbulence was assumed to be a maximum at ground level and its magnitude was recognised as being a function of the ground roughness. Schmidt (1935) suggested that this turbulence. in the form of vortices at ground level. vvas spread upwards in the boundary layer. It was shown later (see Section 2.12) that these vortices were in fact “projected” into the main flow above the ground. thus distributing the turbulence from ground level into the upper part of the boundary layer (see also Pagon. 1935).

.L\diatxrx atmospheric boundq
The uji: of a power spectrum had also been suggested b> Schmidt (19X) as a method of indicating the energy content of the various eddy sizes. The basic theorq relating the power spectrum to the correlations was subxqurntl> derived by TirlOr (1938). The hypothesis of Kolmogoroff (1941) showed the simifarit! of the strtlcture of the turbulence at high Reynolds numbers. that is the similarit: of the small scale turbulent eddies associated with the high frequency end of the spectrum. It was generally accepted that the eddy sties represented in the spectrum could be divided into three regions as follows:



,,/(;>--, \

(a) x low frequency range. containing most of the turbulent energ! : this energ! being transferred by inertial forces to higher frequencies. (b) An intermediate range. or vertical subrange. which follows Kolmogoroffs - $0 law. and (c) A high frequency. dissipation range.


Townsend ( 1931). from work on Hat-plate boundary layers, suggested that the size of large eddies in the Row approached the boundary layer height. He also proposed that rhc boundary layer could be divided Fig. I. Structure of boundark layer tlow lirom Townsend. 1957). into (a) an outer laqer. in which non-turbulent fluid was entrained from the mran flow by the large eddies. (h) an inner later in which turbulent energy was shear instabilities in the main flow (cf. Durst. 19.32). and that they rotated relatively slowly ha\ing vertical created. velocities of the order of 0.10 c,,. It \\as also shown Pricstley and Sheppard (1952) illustrated how mergq was transferred through the different frequency ranges by Panofsky and Singer (1965) that gust fronts have a slope of the order of one due to the xsrtical cvind of a power spectrum. Panofsky and McCormick (1951) showed that spectral shapes were generally in- shear. From studies on fiat-plarz boundary la)ers. Kline dependent of terrain roughness. They also showed that the structure of longitudinal turbulence differed l’r nl. (1967) demonstrated the presence oi secondary from that of vertical turbulence since its length scales. vorticitp (that is the large eddies proposed hq or eddy sizes. lqere greater than those of the vertical Townsend. 19571 in the lower part of the boundary turbulence. The rsistence of eddies of various sizes layer. The> suggested that the action of these on the spanu-ise vorticity formed wall streaks. The resultant was also demonstrated by Deacon (1955a). Extending his previous analysis. Townsend (1957) ejection of Huid from the Ivail region was considered to be the main mechanism for turbulent transfer suggested that boundary layer flows had contra-rotating vortex pairs. moving with the Row. and having bebeen the inner and outer layers (cf. Schmidt. 1935). their axes parallel to the flow direction (Fig. I). Sets In contrast. ths work of Tritton (1967) did not verify of large eddies were assumed to exist both in the inner the existence in the boundary layer of the large eddy and the outer section of the boundary layer. Extensive structure proposed by Townsend. He supgssted that meas~irements in flat-plate boundary la-er flow by the separate descriptions of large eddies for inner and Grant (19%) showed the existence of targe eddies in outer layers mat- be inappropriate. Bradshaw (196s) the Row and the increase of eddy size with increase proposed that the sizes of the large sddies were in of distance from the wall. Finally. Panofsky er al. fact of the same order of magnitude as the boundarc (1958) verified Taylor’s hypothesis concerning the layer thickness. He agreed with Faller (19651concerning transport of eddies at the same speed as the local the origin of these large eddies and that they consisted mean wind speed. of a slow rotational drift of fluid ha\-ing ti: z 010 lo ~~{t~z~7ff~~~~: Although a broad picture of the Row Gf,. structure had now emerged. its detailed flow patterns Panofsky (1969) pointed out that the boundary were still undefined. layer flow over the sea produced very large 2.1.2 Prriofl 1960-197~. It had been shotvn that the longitudinal eddies near the surface and suggested lenpth scal& of turbulence increase. with increase of that over rough ground such eddies were likely to distance from the ground. e.g. Blackadar (1962) probe broken LIP (see Section 3.10). posed that the) increased in proportion to k: To sl~~t~/~iff~i~~~: There is relatively little information &’= Van Karman’s constant) close to the ground and available on the detailed Row structure of the approachedfixed values higher up in the boundary layer boundary layer and some disagreement exists between (that is for r > XC-XXI m). Failer (1965) suggested the work published by various authors. However. it that the large eddies in adiabatic flows resulted from has been established that large scale motions are

present in the boundar\- la’;er (i.e. large eddies exist) u hose orientation is a function of the shear in the mean How and whose degree of rotation is reiativefy slow. The size of these large :ddies is also a function of surface roughness and this will be considered later.

height was generally WI-700 m based on empirical formulae of the form. d = 0.006 Cc1 -._ F where F is the Coriolis parameter (rad s- ‘). Theoretical estimates from Smith (1970) gave heights around 800 m. Finally. Pasquill (1972) suggested that the mechanical production of energ!. tended to approach zero at a height of 600 m and therefore, for adiabatic conditions. it is reasonable to assume that this height should be coincident w?th the top of the boundary layer. To ~777777~~~~~~~: In choosing what ma! be considered as a practical and typical boundary layer height. some compromises must be made. e.g. the height is clearly a function of both the gradient wind speed and the surface roughness. On the basis of the reviewed data for high wind speeds (iit > j--7 m s-‘) which produce adiabatic or near adiabatic conditions. a value of 600 m is recommended as representing the average height of both rural and urban boundary layers. 2.3 Hright 0J’thr cowfualrtskfzr strrss itrwi 23.1 Prriod 158@1972. This height is of interest since it defines the region in which the mean wind profile follows a log-law. From mean bvind measurements in this layer the surface roughness length can be defined. The earlier data suggest values for this height consistently within the range of 30-50 m. However. much higher values have been quoted in more recent papers. particularly in the case of flow over urban terrain. Byzova (1963). for example. suggested a height of about 75 m and Soma (1964) a height of at least 200 m for an urban area. This implies that the log-law can be expected to apply over a greater height range for urban areas and hence it could be more difficult to establish a representative power law for such terrain. These findings were supported by Yamamoto and Shimanuki (1964) and by Lappe i 1965) who suggested that the log-law could be applied up to a height of about 140 m and that it was aiso more applicable as the terrain roughness increased. Constant stress layer heights of about 100 m were also suggested by Deland and Binkouski (1966). Estoque (1967) and Panofsky (1969). By assuming the constant stress layer to apply up to a height of about 200 m. Blackadar and Chaplin (1967) produced a modified version of the log-law which effectively linearised. when plotted. mean velocity measurements which had been measured outside the normally accepted constant shear stress layer. However. it was suggested by Davenport (1967) that such theoretical approaches towards defining the mean velocity profile are suspect because of the assumptions involved in their development, More recently. Panofsky and Petersen (1972) suggested that the constant stress layer could be assumed to have a height of about 100 m.

ths height of the adiabatic boundary IaFer. However. most of them involve the use of empirical constants or coeficients whose preciw values have not been agreed. For practical purposes. measurements are therefore to be preferred and conseqL]ent~y the majority of the references considered below deal with tither observed or measured data. ’ 1 -._. I P&.X/ l&80-1959. Some of the earliest data ivere contained in Dobson (1914) who showed that the boundary layer height a-as CIJ. 4%?-6OOm. with little turbulence esisting abovs a height of about 600 m. In addition Taylor (1917). Schmidt (1918) and Giblett (1932) all suggested heights in the range of 4%600 m. Pagon (1935) derived theoretical values for rural and urban boundary layer heights. of 325 and 525 m respectively. by assuming an eddy siscosity which s\as constant with height. Later in this period Sheppard (1922) and Sheppard and Omar (1952) quoted measured boundary layer heights of ND.and 45@600 m respectively. Most other observations made in this period quoted heights around 600 m. ’ 1’ 196Cr1972. From Section 2.2.1 a _.-._ Period height of 600 m appeared to be an acceptable average value for adiabatic boundary layers. However, Davenport (1961b) suggested that this height was a function of terrain type and proposed; EWfl ill Rural Urban 6(il?j 273 518 cf. 6(tlTj i75 --c [ 525 I Pagon (1935)

.Although no reference for the values was quoted. they are very similar to those given by Pagon (I 935) which are based on approximate theoretical assumptions only. The value of around 300 m suggested for a rural boundary layer is not supported by any previous meteorological data. In addition. it was found later (Counihan. 1970) that if atmospheric and Hat-plate boundary layer data are compared on the basis of non-dimensional height (i.e. ’ 6. for d = 3Om) very little agreement was obtained. whereas a height of 600 m gives very good agreement. Blackadar (I 962) suggested that the ~undar~ layer height was affected very little by changes in terrain roughness; this was further supported by Shellard (1963) who also assumed a mean boundary layer height of 500 m. In addition. Shellard’s (1967) data showed that the height of rural terrain boundary layers was in excess of 300-400 m. Theoretical methods of estimating boundary layer heights. for various types of thermal stratification. were extensively reviewed by Hanna (1969). For adiabatic conditions he found that the boundary layer

.Ad~abarlc atmospheric boundary ia)crs To s~~rn~~ri:~~: It can be concluded a reasonable value for the average constant shear stress layer. 3.4 T/W
2.41 1t7m7 cdocifj~ projilr


that 100 m is height of the

The main problems involved in the measurement of mean velocit! profiles were adequateI> assessed h> Chapman (1919). Although he concluded that most of the data could best be represented b> a log-law of the form. u = II log : + h. a power law provides an equally good tit to most of the data considered. particularly in the case of high winds. Other variations of the log-law vvere suggested later. but these were not generally adopted as they involved the use of empirical parameters Lvhich were functions of both wind speed and atmosphsric thermal equilibrium. e.g. Geiger (1927). Sutton (1932) and Ali (1932). By utilizing the Hat-plate boundary la!sr theor) of Prandtl and Van Karman. a more refined version of the log-law vvas produced by Sverdrup I 193-t).

rrmir7. \fanj laws for the variation of the mean velocity with height have been suggested. One of the earliest was that of Stevenson ( 1880) who proposed a parabolic law.






U, are the mean _


(m s-r)

at arbitrary heights 1, (w) and z1 (VI) respectively. This law did not apply to the lower IO m of the measured velocity profiles. By assuming the application of a power law. power indices of between 0,143 and 0.167 can be deduced from Stevenson’s results for the various rural terrain types considered. A power law representation was later proposed by .Archibald ( 1885)having the form. Ii/Ii> = (I ,,i-_$ a. Later, Shaw (1909) predicted height.
7i7/L7” = ci+c -. C

a linear variation


This \vas assumed to be applicable for adiabatic equilibrium. up to a height of about IO m and provided a method of determining the relative roughness of the terrain considered. However. Sverdrup also pointed out that a Ian of the form. Ii, -= I?? _

where c is a function of the ground roughness. Mean velocity measurements by Dobson (1914) were shown to follow a power law having an index of 0.143. .A theoretical mean wind profile estimated b> Taylor (1915) generally agreed with Dobson’s measurements (Fig. 2).

\ !I
-1 ._l,


(i.e. a power lau-I.




.a OF


200 WIN0




could be applied equally well to most meteorological Since the power la\< could be conditions. mathematically manipulated more easil:. than the it tended to be used more often in log-law, meteorological problems; 1:~ was taken as an indication of the amount of turbulence present. Generally. a value of 0.143 was regarded as applicable to rural terrain. e.g. see Sutton (193-t). Rossbq and Montgomery (1935) and Pagon (1935). Paeschke (1927) quoted extensive data on povver indes values for flows over man> t>pes of terrain. However. these appear to be mostl) overestimated because the! were based on measurements made too close to the ground. This type of ovsrsstimate is common to many papers, especially in the analysis of measurements of mean velocities in urban areas. Further support for an index of 0.143 for rural areas was given in Frost (1947) and Sheppard i 1947). The most important modification to the above laws was indicated by Sutton (1949) as. u : - tf =;1og..-. c’* -n which took into account the zero plane displacement (d) when considering large roughness slements (see also Paeschke. 1937). Generally. in the period 1950-1959 I I = 0.143 was quoted extensively as applying to rural terrain. The most relevant data were included in Collins (1955). Deacon (1955,) and Kamei (19%) with more detailed data on one site included in Lettau and Davidson (1959).

3 WIND Fig. 2.






11 PER



100 WHO






Theoretical and measured mean (from Taylor. 1915).




COL>IH.A\ area. the range for urban and “rough” terrains was 0.2 I-040. 2.4.1 Prriotl I36c 1972-1lrha~ crjrtl or/~/. rc~rrah. Suburban and urban terrains w2re considered by Davenport ( 1961b. 196-t. 1967) who has specified indices of 0.28 and 0.40 respectively: his most recent data suggested 0.36 for an urban area. However. Shellard (19631 suggested that these high indices were neither realistic nor representative of urban areas. The most rscent data presented in the E.S.D.U. data sheets 72026 (1971) again suggested 0.35 as being repressntative of an urban area. However. the majority of th2 urban data asssssed here suggest fairly conclusively that the power ind2s for a typical urban area should be about 0.%0.30: as an example. the following data ar2 quoted. I,‘% London Louisville 0.29 : 0.16 Minneapolis : 0.3I

Th2 choice appears arbitrary as to whether th2 mean vslocity profils is representsd by a log-law or a power-lava. Thz lower ?@jO m of the boundary layer is b2tter reprrsrnted by a log-lava. and it is clearly incorrect to try to d2duce a power-law index from m2asurements made in this height range. Hovcsvsr. ths power law seems to give a better fit to most of the data ovsr a greatzr height range and for high wind conditions, Hsncr it was decided to adopt the povver-law for the final presentation of the data in this rzview. To SUUIWW~X: The power index for flow over rural terrains lies m the rang2 of O.IJ.1-tII67. A value of (1.14.: is the most liksly value for typical rural terrain. 2.-t.? Prriotl I960- 197?-r1& rerrairl. A considernbl2 amount of data is available from rural terrain slt2s in this period. However. they will not be considered in detail here since th2y do not alter the conclusions previously reached. Th2 data are tsbulatcd in 4ppendi.x 2 and are included in the final prsssntation of all th2 results. 3.4.3 Prriotl I YSG 1959~rfrharr a/fd or/w rerrai~~ The ass2ssment of mean velocity msasurements from urban and other rough trrrains is more difficult because: (a) Results for such conditions are scarce. tb) Many of the available results represrnt local topographical effects rather than particular typrs of tsrrain. .LIeasursmsnts mad2 by Mildnsr (1933) near Leipzig vvtlre among the earliest made in “rough” terrain. They may be taken as typical of a suburban site and a power indes in the range of 0.X-0.35 gives ;I good fit to the data. An urban case referred to by Rossby and Montgomery (1935) was best represented by an indes of about 010. Values of 0.36 for Strasburg and 0.40 for Tokyo were suggested by Paeschke (1935) and Shiotani and Yamamoto (1948) respsctively. However there is insufficient detail pressnted as to the instrument siting relative to the local topography for a reliable assessment to be made of these measurements. Hellermann (1953) suggested a value of 033 for a typical city site and Kamsi (1955) the same value for Japanese towns. In the latter case it is probable that ths measuremrnts were influsnced by the presence of nearby buildings. The same criticism applies to the Copenhagen msasurements of Jensen (3953) from which a power index in the rang2 of 0.34-0.35 was dsducrd for th2 city centre. An esample of an overestimate of the power index for the Brookhaven sit2 can b2 deduced from De Marrais (1959) and Singer and Smith (1959). Although a valus of 0.28 IS prrsently taken to rrpresent this site. a closer examination of the data suggests that power index of 0.30-0.23 is more applicablz. The site consists of soms woodland having trees LIP to about 10 m in h2ight. and this can b2 regarded as being similar to a suburban site TO .s1rm17ari:~: Although it was not entitely clear vvhat was the bsst pousr index for a typical urban

I% Nsw Orleans : 0~231 Philadelphia : 0.28 St. Louis Tokyo
: D2Y : i>IYj

: 0.2SY

To .summari~~~: The appropriate power indices for the various terrain types can only be detzrmined by considering all of the available data. The data suggest a power index of 0.21-0,?3 for a suburban area and a valus of 0.28 for urban areas.

2.5 71~ rougIm05 /r,rgtir The magnituds of the roughness length can be derived simply by use of the log-law.
1( L.* = I/k

-_ d log<, :-0

Reliablz estimates are difficult to obtain since the roughness lengths are a function of f2tch. atmospheric thermal stratification. to some sxtent. and of wind speed. unless.

However. thers is some evidence that this criterion is a function of the “type” of roughness being considsred and therefore it cannot be taken as a definitr guide. 2.5. I Pcviorl IWI& 1959~-I.urd rerraiu. Thers are sufficient data available her2 to deduce typical values. This is particularly true of mars recent data when factors such as fstch etc. were usually taken into account. However. it is of intsrest to look at some of the earlier data. For esample. it is possible to obtain typical rural values from the measurements of Stevenson (I 580):

z,(m) 0~001-1 0.0’7 0.048

“Open Ground” Corn (/I, = 0.3m) Corn (ii, = 1m)

which are indepsndent of wind spred. Values derived by Sverdrup (193-I). although the terrain description

.Aduhatic atmospheric houndarb la!zrj

,-.. ‘\







same :&ml
;:g o&9




Short mown grass Open Grassland “R&itivel~ cairn WJ”

The estznsivs data presented by Pacschke (1937) allowsd for the effect of the zero-plane displacement in sstimating the roughness lengths. He quoted.

for terrain a.ar>ing from snow-covered ground to fields of beet and cereal crops. Frost (1947) quoted values of 001 and 0.026 m for sea and open country respectiveI>. Sheppard (I 947) and Deacon (1948) summarised most of the available data on roughness lengths from uhich it can be deduced that for rural terrain,

In a further example of allowing for the zero-plane displacement Pasquill (1950) determined a roughness length of OXI m for grass 0.15 m tall. Shiotani (1950) presented data for terrain covered by grass and tegztables as.

Data quoted by Deacon (1953). Sutton (195jy ‘and Lettau (1959) also lie in the range of values alread) quoted. Deacon (1957) suggested that Nikuradse’s criterion. when applied to grass roughness. should be modified to. -


> 40.

but no other data to support this have been found. From the above data it is possible to deduce reliahls roughness lengths for particular sites; e.g.

: Cardmgton

:,,(ml : OQG2

: O-01

: O’Neill : Brookhaven : IGO.

for these sites the power law indices were aiso known. To SMWIW~:~:rural area roughness lengths should fall in the range.

2.52 Periotl I SSO-1959-&a/I rerrni~. One of the first values quoted for urban terrain was I m by Rossby and Montgomery (1935); they also suggested a value of 3-Z m for “large roughness”. Shiotani and Yamamoto (19%) quoted a value of 4 m for Tokyo. They also suggested that for urban areas.

Later. Kamei (19%) gave a value of 1.5 m for the roughness length of Tokyo. To .~~~~~IJII~~~~~~,: from data of this period. only an approximate guide for urban areas can be derived. Ia Q I(, (111) 4.0. ,< (but see summark to 25.3).

196O-i9~1. Rather than deai 3.3 Pt~rioti individuali! with the large amount of dara from this period. which hat? been tabulated in ,Appendix II. just some of the more interesting bvork and conclusions will be noted here reparding the roughness length and its measurement in both rural and urban tsrrains. Some theoretical estimates of roughness lengths werr‘ presented by Panofskl. Blxkadar and McNeil1 (1960) which v\ill be considered in Section 3.1. Jensen (1961) classified the roughness length and the displacement thickness as a function of vegetation height. Rauner (1961) showed that the roughness length of a forest was a function of wind sped. due to the fact that at higher wind speeds the wind penetrates mars through the trees. He also determined the relative roughness of a forest with and without foliage. ,An empirical form of the variation of the roughness length with terrain tbpc \cas suggested b\ Davenport (1963). The work of Oliphant and PanoBkg (1965) illustrated a point of interest obsr\ed when determining thz roughness length of the BrookhaLen site. Their data shoived how t\\‘o separate estimates of this length could he derived from measurements at the same site position. One estimate >,:pe:tred to be appropriate to the IocaI flat gro~md. and the second one to the wooded area upstream: data from both estimates were used to obtain a mean site roughness length. Barry (1966) indicated that it teas posjlbie to obtain wide variations in estimates of the roughness length for any particular site. The data he as=swd appear to apply to a very restricted height range and therefore his conclusions cannot be taken as being completely reliable. It is also considered that large discrepancies are possible in estimates of the roughness Iength made by using the modified log-law derived. on a theoretical basis. and proposed b> Blackadar and Chaplin (1967). This should be particularly noted when considering the rcssnt papers of Harris (1972) and E.S.D.U. 72016 (19-Z). Fichtl (196Sa) in analysing data from the Kenned! Space Centre. noted that when there ax variations in the local terrain it is essential that the roughness length should be defined as a function of wind direction. With regard to urban areas. \funn (1968) drew attention to the problem of dctrrmining realistic roughness lengths and pointed out ths importance of choosing measuring sites which were not intluencsd by local efIects. The available data indicated that the roughness len_gthcould be assumed to be independent of atmospheric thermal stratification. r.g. Blackadar i’f a/. (1969). The dependence of the roughness length on ths density distribution of roughness elsmsnts vlas considered by Lettau (1969) and in more detail by Wooding iit ai. (1969): however. the c&t of fetch was not considered. Both of these quantities are of importance in the definition of suburban or urban areas. Helli~~rll (1970) przsentsd furthsr data on the variation of the roughness length ivith terrain t>pe:




in this case the urban roughness length of 0.75 m quoted was particularI> low and seems more applicable to a suburban area. In addition. thz uork of Harris (1972) and the E.S.D.U. (1972) quotsd very low roughness lengths for the terrain types they considered. This is probabl! due to use of the modified log-law as suggested b> Blackadar and Chaplin ( 1967). To smttwix: typical roughness lengths for suburban and urban areas are about I m and Z-3 m respectively.



Fig. 3. Variation

of Reynolds stress with wind speed (from Deacon. 1957).

2.6 T/w Rrrttoitl~ .strc,sscs This is one of the most diticult quantities to assess since the available data ars not vsry extensive. and in the case of urban areas are particularly sparse. However. If it is assumed that the variation of the stresses through the boundary layer is similar to that of a Hat-plate boundar! layer. then sufficient information is available to define their order of magnitude in the constant stress la>er for rural and moderately rough terrains. It is then possible to define bb extrapolation. with some degree of reliability. the stresses associated with urban terrain. 2.6.1 Prriod lSStbl9j9. The earliest assessments of the ground level Reynolds stresses were included in TIlylor (1916). which gave 7, -oGO11 < - II’\\.’ I ; < 0~0020. These
\vhere the velocit!

The data quoted above refer mostly to rural terrain. However. Deland and Panofsky (1957). comparing data from Brookhaven (I,, = 1 m) and O’Neill (:-(, = 0.01 m). suggested that the Reynolds stresses based on local velocity vary by about a factor of 10 between these two sites; Lsttau and Davidson (1957) quoted a value of 00017 for the ONill site. Finally. in this period Vinogradova (1959) gdw a value of OGOO4 for the stresses on a water surface. To sztttmmix: neglecting the svtreme cases of the above data. it is suggested that rural stress values should lie in the range 7, 0~00~0 < - U’W’L ;, < 0~0030. at or near ground level. 2.62 Period 196G1972. Data from urban sites remained sparse (see Appendix 4). but some broad generalizations are possible. There was some evidence that the scatter of the available data increased as the roughness length increased. This seems plausible. since the larger roughness elements would be expected to produce greater local variations from a mean value of the Reynolds stress. For rough terrain the data of Davenport (I 964). based on the free-stream velocity, indicated that the Reynolds stress decreased with Increase of the roughness length, in the range of roughness appropriate to an urban terrain: no reason can be suggested for this. Pasquill (1970). from accumulated data on the Reynolds stresses. showed that this quantity increased with increase of roughness length up to at least 1 m. and was not very sensitive to variations in the free-stream velocity co. From this paper, or from Smith (1970). the ratio of urban to rural stresses can be determined as 1.46-1.56. for roughness lengths of 23 and 0.10 m respectively. and so the existing data could be extrapolated to obtain Reynolds stresses for urban areas (i.e. 2 < Z,) (111) 3). 6 To srrmmvix: from the combined data. the range of Reynolds stresses applicable to rural and sea areas can be defined respectively as. 09020 ,< - 1r’bv’:C.i) d 0003 and.

applicable to open countryside ‘rs’,,is assumed to occur at a height of 600 m. Scrase (1930) dsrived a value of approx. 00315 at a height of 19 m above the ground: this can also be regarded as the appro.ximate value at ground level. since the Reynolds stress was considered to be constant (to within ccl. 6 per cent) up to a height of about 50 m above ground level (e.g. see Calder. 1939). Further measurements were presented by Sheppard (1947) in the form of a drag coefficient. C,, = 2 (-Z/ii;).



mhere Ir, is a reference velocity. The range of stresses generally applicable to rural terrain can be deduced from the above data as,

For Row over short grass and sea. values as low as 00010 were quoted by Pasquill (1950) and Sheppard (1952) and a value of OGO2-1 by Shiotani (19%). Hay ( 1959) gave a value as low as 0.006 for How over the sea and Monin and Obukhov (1954) suggested a mean value of 00325 for rural terrain. .A value of O-C005 was given by Rider (1954) for a mown grass surface. which agreed with the data given in Pasquill (I 950). Further ralues for open country were given in Ellison (1956) and Deacon (1957) of OX013 and OQO22 respectively; Deacon’s data also showed the degree of scatter to which these measurements are subject (Fig. 3).



where r,,

is assumed

to occur at 600 m

s2e also Robinson (19531. Thz ratio of th2 vsrticaI to longitudinal turbulenc2 intensity of 0.5 vvas dsrived from JlcCrsady (1353) and others. whoa turbulence: m2asurements also fall in ths rangss alrsady quot2d. Shiotani (1953) for snow-covsr2d terrain gav’e 0.10 G ~ (2) !1 < 0.16 intensitirs

Ti smvnmizc: longitudinal turbulsncs for rural arsas fall in the range.

0.10 $ \ (Z,

ti $ 0.70

for httights betwssn 3 m and 30 m abovs ground Isvel. 1.7.2 Period I SSt)- I9j%t&m trvnirl. Som2 of th2 first m2asuremsnts of longitudinal turbulrnce intznsity made in an urban area wer2 przsented in Shiotani and Yamamoto (1912). These m2asuremsnts fall in the range.

0.20 d , (Z) u < 0.30. A valus of longitudinal turbulence intsnsity of 0.5, near ground level. can be drrived from Cramer (1951) for an ar2a having “large” roughness. On th2 basis of the vsry few data from this psriod it can be assumed that urban turbulence intensities should Ii2 in the range. 0.20 < ~ (LI.z),li < 0.35. th2 above data wer2 considerably Howevsr. augmsntzd during 1960-1977. AI1 of the data on these measursmcnts are pres2ntsd in Appendi\ 3. 2.7.3 Period 1960-1971. The data from this psriod (see Appsndix 3) gsnrrally confirmed th: conclusions drawn from the earli2r measurements. Ttxrefore only some general points of interest concsrning th2 measur2msnts and sstimation of turbulsncs intensity will be considered here. It had bezn shown (2.7.‘). that ths variations of turbulsncs intensity with height were comparabls to those of flat-plate boundary layers; th2 atmosphsric data was then only available for a rsstricted height rangr. This similarity was verified o\:r a grratrr height range by ths work of Swanson and Cramer (1965). who showsd that both the longitudinal and lateral intznsitiss of turbulcncc dscrsased with increax of height up to IO m abovs ground level. Pritchard (1966) showed that the vertical turbulence intensity was approximately constant aith incrsass of height up to about 370 m: he also assumed that the turbulence was isotropic at and abox this bright. Moors (1967) also demonstrated that ths turbulence was isotropic. for short wavelengths. above a height of about 200 m. Ths data of Harris (1972) shovvsd that th2 longitudinal turbulence (, ?) was strictly not invariant with height. in th2 height range of IS0 m considered. This fact is of particular rrIe\ance in ths application of th2 first of thz following sxpressions. \ (71 c:* = ‘4. ~ (7)/L.* = 5. \ (7) L:, = C.


Fig. -1. Variation ofgust structur? with height (from Scrasr.

2.7 7-/M,irltol.sirl~ of’ tlrrhirlerfct’ Th2 rat2 of production of turbulence and its intensity is a function of ths Reynolds stresses and the mean velocity profile of the flow being considered. 2.7. I Prriotl I SS@ I959-ixral fWxi/l. It was rzcognissd in ths sarly literature that turbulrnce was a function of both surface roughness and h2ight abovs ground level (Fig. -I). It was also assumed that all three components of turbulencr wer2 of equal magnitude. Howevsr. Scrasl (1930) showed that the ratio of thr three componsnts was as follovvs. , F:, F:, II..? = 1:0.73:0.46.

(c.f. typical Hat-plate data which gives ratios of I :0.75 :O.W). These: ratios applied from about ground 12vel up to th2 hsight of ‘0 m considersd. Th2 magnitud2 of ths longitudinal component was establishrd by Best (1935) as. \ (?)!U - 0~1~5-0~16.

for op2n country-side. Hence. the corr2sponding values of the othsr two componsnts could be derived. Up to the bright Best considerld, the ratios and variations of the components agreed with the pip2 tlow m2asurem2nts of Fag2 and Townsnd (1932). Many other authors at this time also dcriced the ratio of thr lateral to vsrtical turbulence intensity as being I.Cl.6. Shiotani and Yamamoto (1932) quotsd values of about 0.13 for rural terrain longitudinal turbulence intensity. Additional data for rural terrain were presznted by Shiotani (1950) which fsll in ths rang2 0~1~0~11. .A valus of the turbulence intensity over water of 0.19 was quoted by Sheppard (1952). Fairly eutensivs mrasurements of lateral turbulence given by Friedman (1953) vsrified that the ratio of lateral to longitudinal turbulence intensity was 0.7j.

which are used est2nsively to obtain estimates of the turbulence intensities. A comparison of estimates.



using these sspressions. with measured data show thar they arc‘ reason&l>- rzliahlc. However it should be noted that the measured data wers mainly those available for flat and rural terrains. Lumley and Panofskl (1964) suggested that such estimates were accurate to 420 psr cent. and that although the values of the constants .-I. B and C. in the above expressions. should be independent of height. that they may be dependent on terrain type. It is assumed here that this independent-of-height condition can only apply in ths constant shear stress layer. where it is abo usuall> assumed that the turbulence components are reasonably invariant with height. This dependence of .-Lon terrain type. or roughness length. was shown to some e.stcnt by the work of Zubkovski and Kravchenko (1967) who demonstrated some decrease of .-I as surface roughness increased. On this basis. the abox expressions can b? expected to overestimate the turbulence intensities associated with large roughness lengths. Panofskv (1969) later pointed out that both rt and B had shown a systematic variation from site to site which suggested that roughness a&ct?d their bchaviour. Teunissrn (1970) used the above expressions to estimate the turbulence intensities through the full boundary layer depth. for v;irious degrees of surface roughness. but such estimates should probably he restricted to the _. . constant stress layer. The mean vaiues oi these constants derived from all the reviewed data are.

The ralidit! of the above theories b&as checked by the sxperimental work oi Drkden { 1943) who measured the power spectra of wind tunnel turbulsnce. The shape of the spsctrum was eventually defined b- Von Karman (19-E) in a form which has not been notabiy impro%sd on.

It was generally agreed that the greater part of the turbulent energy was contained in the low frequency range of the spectrum. i.e. in the large eddy sizes. The energ! transfer processes through the complete turbulence spectrum were later defined in physical terms. e.g. see Priestley and Sheppard (1952). The existence of a “spectral gap” which consenienti> separated the mean and turbulent motions in the m~cromct~orological. or gust. range of frequencies was initial!) shown h> Panofsky and van dcr Haven (1955). Deland and Panofsky (1957) subssquzntly showed that the longitudinal spectra were approsimatzly invariant with height. Eventually a complete spectrum of the longitudinal velocity (Fig. 5) was presented by tan der Hoven (1957) which covered the micro and mesometeorolog~cal ranges. This is now thz classical spectrum shown in most papers uhich refer to the atmospheric boundary layer. It showed that averaging periods of I i-30 min should be sufficiently long for measurement of representative mean wind velocities. It was also suggested that the .-I = 2.5. 5 = 1375. C = I .Ei spectral gap occurred at higher frequencies in fiows from which. over rougher terrain: this implies a reduction in the length scales of turbulence with increase of terrain roughness. The majority of the available data confirmed that the slope of the spectrum was appros. -50 at the X3.1 Prriorl IYSO-19j~~o/~~~fIl~~~}~~6 c~~~?~o~I~~lf. high frsqucncy end. in agreement with Kolmogoroffs The work involved in defining the form of the power spectral density of the three velocity components did theorem: confirmation was also obtained from the Right measurements of Notes (1957. 1959) and of not progress as rapidly as that on the measurement Henry ( 1959). of other quantities. To s11177177wI’:~~: The general form and characteristics After the work of Scrase (1930) it was suggested of the longitudinal spectrum had been established, by Giblett (1932) that the energy of eddies having 2.52 PLG%~ lS~~~9j~~~~~~ff~ rlltfi crrtirni various time periods could be represented by an co~r7pm7r77rs. There is little worthwhile information “energy spectrum”. Some attempts were made by Schmidt (1935) to define the high frequency end of available on laterai spectra; that available on the vertical spectra has in many instances been used in such a spectrum. This concept of a power spectrum spectra. For was defined in more detail by Taylor (1935) who comparisons with the longitudinal suggested that it could be resolved into harmonic components and that its integrated value i>) could be regarded as being the sum of contributions from all frequencies (0); he defined F(U) such that I F(n) d/l = I. i0

where F({7) is the normalised poiver spectral fxxction. The high frequency end of the spectrum u-as defined by Koimogoroff (1941) and was shown to obe) his similarity law such that.
r7.977) % 17-1: 3,

5. Horizontal wind-speed spectrum at Brookhaven Satlonal Laboratory at about 100 m height.






Brook-haven. measurements at from e\ampl<. Punofsk) and McCormick (19511 defined some ot’ the general propc’rties of the longitudinal and vertical the> showed that at IOM jp<CtlX. In particular. fr-quencics there was comparativeI> little energy in the vertical spectrum in comparison to that in the longitudinal spectrum: both spectra were shown to be similar at high frequsncies. It was implied that ths eddy sizes associatsd with the vertical component increased with increase of distance from the ground. 1.e the \ertlcal spectra ivill not be invariant with height. Deland and Panofskb (1957) suggested that the b?rtical spectrum shape could be represented bb.

( 1968) established the presence of more low frequent! tnergq than in similar measurements o\sr land; this was further supported bq the data of Shiotani (1968). Some additional forms for the longitudinal spectrum were proposed at this time by various authors. Harris (1968) suggested the form.

which is similar to that proposed b> \.on Karman (194). Another form was proposed b> Fichtl and McVehil (1969) as followx

(where L is a length scale dsrived semi+mpirically) It was concluded b\ Panofsky (1969) that. due to .-\p,tin most of the available data confirmed that the the wide variation in spectral shapes. ths application jlopes at the high frequency end of the spectra were of an> empirical spectral form to a particular site approu. -5 3. could onI\ be approximate. Pasquiil (1970) i% .SII~JWI~W~X: general form for the vertical a recommended the use of a more simpl: spectrum spectrum had been established. expression which would appl! mainI> to the inertial 23.3 Pt,r~otl 196~-1972-lo/1yitlrtli,1n1 CON~OW/I~. sub-range and for heights up to about ILWm. There was a considerable increase in the measurement and anal\& of po\ver spectral densities in this period: rhe more interesting points only are discussed here \L1 1 L* since po\vsr spectral data has generally been He suggested that the power spectral densities at pr:viousl! rsviewed. e.g. Kaimal er nl. (1972). -lower frequencies \vere too variable From the work of Davenport (1961a. b) the to define accurately; a possible esplanation for this iariabilitk longitudinal spectrum lvas expressed in a revised form was given by Owen (197 I). Finally. thr most recent a.3. spectral data for the longitudinal component wfre given in Kaimal et al. (1971): their proposed form was shown to agree \\ith the full-scale data considered. However. This form of the spectrum underestimates the energ) these data. having been presented only recently in the literature. have not in the IOU- frequency range and therefore does not been fully assessed here but are noted for agree completely with full-scale spectral completeness of the revielv. measuremsnts; the invariance of the spectrum with 2.8.1 PetGtl l960- 1971-_(arr~I nd hsight was also assumed. wrricd COI~I~~I~~I~S. T/w lafrr-tr/ ,fimuclri~7q tdocir!.: There are Pond (1966) demonstrated thdt Kolmogoroffs law verv few data available on this po\ver spectral density. applied to power spectra over the sea down to values This is mainly due to the fact that there was not of y’ii as low as 0.0082 m-’ and various power very much interest in this component in structural spectral msasuremcnts showed that this law was applicable over a much wider range of frequencies problems. However. the general charactsristics which can be defined are outlined in ths follo\ving text. than anticipated. Elderkin (1967) established Elderkin 11967) sho\ved that the -5 3 law could applicability of the law down to 11,Ti 0.029 m- ’ for = be applied to the available measurements in the tlow over flat terrain. On the basis of this and other data it appears that the frequency range over which the inertial subrange. Singer et [II. ( 1967) showed that the above law applied is a function of terrain roughness. lateral spectrum. in terms of energy contsnt. lay in position betbvsen the spectra of the This seems plausible since some re-distribution of an intermediate longitudinal and vertical velocities. This point was snergq would be expected to occur as surface roughness increased. However. measuring techniques also adequately verified by the data of Fichtl and are probabl) not capable of detecting these spectral $lcVehil (1969). In addition. Panoijky (1969) suggested that these spectra should be invariant with dit%rences and Davenport (1967) concluded that qWXI’:l measured over rural and urban terrain were height. as Ivere the longitudinal spectra. The most basicall) similar. up-to-date are contained in Kaimal rt al. I 1972). Singer. Busch and Frizzola (1967) adequateI> 71~ L.L,I.II’C(II,~IICIII(IIIJI~ wlocir!,: The form proposed established the invariance of the longitudinal by Panofskq and McCormick (1960) aas basicall) spectrum ivith height. that is the fact that the peak similar to that previously given bv Deland and Lalue of 11iT is independent of height. E.\tensive Panofskg (1957): this showed that thi spxtrum was measurements over the sea by Busch and Panofsk! height dsprndsnt. Various other forms of this



cOL\IHA\ anallsed b? Panofsk! and ?ilares I I‘%) who derived an expression for the cospectraf shape.

spectrum were proposed mainiy b> authors concsrncd rvith the ana&sis of vertical gust loads on aircraft. e.g. Zbrozsk f 1961) and tappe f 1963). Elderkin (1967) establlshed the peak value of the reduced frequency to be about O4O. compared to about O.O3 for longitudinal spectra: this implies that the nx$ority of the energy associated with vertical spectra is at higher frequencies. The measurements of Kaimal and Haugen (1967) generally supported the findings of Elderkin: they also showed that these spectra were height dependent in as much as the peak frequency decreased with increase of distance from the ground. This implies that as the effect of ground proximity decreases. the vertical scale of the eddies can increase. i.e. reduced frequent> (rr:,,:‘ii)would increase with height. Finally, Busch and Panofsky (1968) presented a slightly modified version of the spectral form previously suggested b> Panofsky.

The quantity L. which is the value of the reduced frequency at the cospectrum peak. was taken as 0.08 for adiabatic conditions. This quantit!. however. was found to be subject to a considerable degree of scatter which covered the range.

The most recent data of :\/Iiyake vc rri. (1970) and Sitaraman (1970) verified the validity of the cospectrai form proposed by Panofskb and Mares (1968). The above form of the cospectrum is generally used. although its applicability for heights greater than about 50 m has yet to be established. fhs more recent data of Kaimal r’rni. (1972) suggested.

rvhere _/, 2 0.32 for adiabatic conditions. This is the form of the vertical spectrum most often ussd. The most recent form has been given in Kaimal rf ai. (1972).

which is similar to that proposed by Panofsky and Nares.

The relevance of the Reynolds stress cospectrum. in the context of defining the Earth’s boundar) layer. is that ir indicates the frequency band in which these stresses are of importance. 2.9.1 Prriotl I88@-1959. Early discussions on the cospectrum are included in Panofsky and McCormick (1954) and Panofsky and van der Woven (1955). Deacon (19Sj.b) showed that most of the cospectral energ! was contained in the range.

and this has been adequately verified by recent measurements (see Panofsky and Mares. 1968). It also showed how a regular eddy pattsrn in a Row Deland and Panofsky (1957) suggested that as the could be distinguished from such data. height of observation increased there was an increase Most of the later data on length scales supported of energy at low frequencies and a decrease at high TayIor’s deduction regarding the increase of length frequencies. This is consistent with the data of Kaimal scale with height. e.g. Giblett (1932) gave Llr, as about and Haugen (1967) concerning the characteristics of I20 m at a height of 15 m. One of the few values vertical spectra. Panofskv and Deland (1959) further of the vertical scale of turbulence (Lu,) was showed the expected rapid decrease in the energy determined by Schmidt (1935) as being of the order content of the cospectrum at the frequencies where of 15 m at heights iess than 6 m. Additional there was very little low frequency energy in the theoretical work by Taylor (1938) provided a spectrum of the vertical velocity component. relationship betwern power spectra and the 2.92 Prriotl 1960-1972. This period produced correlation coefficients. suFIicient data for the cospectrum to be defined. at least over a restricted height range. The first relevant data were presented in Monin t 1962) who confirmed the findings of Deacon (1955b) regarding the / ‘nrr\frequency range of the cospectral energy. This was R(s) cos ds. ii also verified by Elderkin (1965). The majority of the available data. for heights less than about 50 m. were where R(s) = correlation coefficient and f(n) = power

2. IO.I Prrid I SSC 1959. The mean eddy size in the longitudinal direction (LuJ NX deduced initially b) Taylor (1915) to be about 70 m at a height of 10 m. Extrapolation of more recent data would suggest a value of the order of 100 m at this height. which gives fair agreement with Taylor’s estimate. He also deduced that the mean cddq size increased with increase of height above the ground. for the simple reascm that “they have more room to gJ0~“. His later work. Taylor (1920). on the concept of correlation m~asur~mcnts. showed that turbulence scales could be determined from. -r LL/.,= u R(r) dr. i (1

.Adiabatic atmospheric bounder) lalers spectral density. Hence. when z = 0. the mean largest eddy size is defined as.


The maJorit> of ths data were concerned with the lsngth scalt Lu,~ and Pasquill (1961) showed that these could be derived from spectral measurements since.

The nest significant were those of Shiotani determined.

length scale measurements and Yamamoto (1915) who or ~22. 2.g. Pasquill and Butler (196-I). This was derived bq’ assuming an exponential form for correlation curves: in practice the exponential form has been found to apply more often than not. The main difticult> can occur in defining the spectral peak: however. checking estimates from the above expression against length scales derived from auto or space correlations has shown its validity. From some of the available data Pasquill also deduced. LUr I -_. Blackadar (1962) assumed that LI, increased with increase of height LIP to CLI.200-300 m and that it was of the order of I00 m at greater heights. ,A reference to the length scale was contained in Singer ( 1964) u ho suggested that. Llfr = 0.3 Ll& It can be shown fairly conclusively from analysis of the data presented bq Berman (1965). and others. that Lir, decreases as surface roughness increases, 2.g. Site Cardmgton Round Hill Brookhaven : -(Am) 0.01 Llc,(m) s?. 36 AmI I5 16 I6

‘for heights up to 50 m In rural terrain: the! also quoted a value of the order of 100 m for urban terrain. From Hat-plate boundary laher work Laufer (1950) suggested that ths length scales should increase with increase of height up to ca. 0.X-0.60 of the boundary layer height. Examples of other published data on length scales from various sites were: LllJrnl II.5 12-15 30 70 Am) z 2.5 IO 35 Source Sheppard (1952) Cramer (1952) Shiotani (1953) Webb(l955).

Most of the available data were reviewed b) Webb (1955) who suggested that the variation of the length scale with height should follow the lau.

up to a height of about 100 m (Fig. 61. A conssrvative extrapolation of the measurements available ~rp~to this time suggestsd that IJI, should be about 200 m at a height of ICH)m. Shiotani (1953) suggested that the three dimensional form of individual eddies should result in. Lu, > L.11,> ,!A, in the lower section of the boundary lajer. Many other values of the length scale IA,, at various heights. can be sstracted from. e.g. PriestIe! (1952). Robinson (1953). Taylor (1955) and Hay and Pasquill (1954). Since these measurements agree with previous data ths law proposed by Webb (1955) was representative of the data from this period. However. it included effects due to variation in surface roughnesses benveen the sites considered. 2.102 Prr-iotf 1960-1971. 7hr le,~grh x&s Lu,. Lu, a& Lu,: FairI! extensive data on the turbulence length scales were obtained during this period. Some of those data and the laws relating to them are considered below.

: 0~04-0~ IO : 140


In addition to the laws noted previously. several others were proposed for the variation of Lu, with height. La\\ Source
Lll, % 1” z4 LU< % Pn

Ll,, T 1

Berman (1965) Panofsky and Singer (1965) Zbrozek (1965).

It was also suggested by Zbrozek (1965) that Lu, increased as the height increased up to about 300 m. The wide Lariety of indices observed is no doubt due to the fact that the length scale was not considered to be a function of surface roughness. The rslativs sizes of other length scales of turbulence were deduced in a gznsralised form by Pritchard (1966) as.

Fig. 6. Variation of length scale with height (from Webb. 1955).

He also assumed that these length scales were functions only of height and thermal stratification. but pointed out that some authors assumed that “greater roughness produced greater length scales”. which is Cledr!y inconsistent with the reanalysed data of Berman and other workers. Close to the ground the variation of IA, with height cannot be expected to follow any of the above laws because. as shown by Smith (1967). it decreases very rapidly near the surface.

Reliable data concerning ths variation of f.lr, with surface rouphnzss can be deduced from Busch and Panofsky (1968). r\nothsr law. concerning its cariation Lvlth height. kvas glvsn b> Fichtl (196s) as.

Fichtl and McVehil (1969) suggested that LID, decreased at heights grsatsr than 100 m and showed the validity of sstimating f.u, from. L[, = L “‘ 2n il I1 p, \h. Finally. the recent work of Colmrr

(1971) propoxd.

remained constant with further incease of height. Pritchard ( 1966) sugersted that Lbv., increased with hsight up to about 120 m about: ground Ie~el. and then remained constant 1~Ith further increase of height up to about 370 m. Kaimal and Haugen (1967) proposed that LK, should sither remain constant or decrease uith increase of height abotz ca. 200 m. For heights in the range of U-50 m. Singer <‘r al. ( 1967) shousd that LIV, increased linear]! with height; at yeatrr heights its rate of increase was less. This result was supported bq the data of Panofsky (1969). by Teunissen (1970) Finally. the general revieu proposed. L\r, - 04 Z, (cf. Pasquill. I96 1)

In ths more recent literature. various other contlicting opinions have appeared regarding the effects of surface roughness on the scales of turbulence. In particular. the review paper of Teunissen (1970) stated that change of surface roughness had little effect on the length LUG, but that “large scale non-uniformities” of the Earth’s surface tended to increase them: the latter statement is plausible and is supported to a certain extent in some of the literature. He also concluded that. for heights greater than about 300 m. the length scales were independent of terrain type. However. no reason was given for the wide scatter of data below this height. In contrast to the above conclusions. the f%-plate data of Antonia and LLlston (1971) showed that increased surface roughness resulted in reduced length scales. The semi-empirical theories of Davenport (1961) and Harris (1971) predicted that Lu, increased height increased as both roughness and monotonically: neither of those predictions agrees with the measurements. Harris ( 197 I ) assumed. from homogeneous isotropic turbulence theory. that the following relationship could be applied to atmospheric turbulence. Lu, = hr = 0.5 LUG However the available data, e.g. Shiotani (1967) and Deacon (1971). showed that more appropriately. LU, = 0.3 - 04 ,$ and

and this was later confirmed by the data ot’ K’arner (197’). jr, swmurix: Lw, is insensitive to chanpes in terrain roughness: the variation with height can be taken as. L,r, % z. in the constant shear stress Iaher.

To summmix: Lu, decreases with increase ot surface roughness. increases with increase of height LIP to ca. 2C+300 m. and thereafter decreases for further increases of height. becoming independent of surface roughness. T/W Irngfh SC& Lbr,: Some data were also available on the variation of the length scale ZJV, as a function of height. Pasquill (1961) using data from various sites. derived.

Lumley and Panofsky (1964) suggested that Lw~ increased with height up to ca. 100-200 m. and then

It is convenient to be able to e.xpress the probabilit) density distributions of the fluctuating velocities in terms of a normal or Gaussian distribution. Some of ths earliest data u’c’rc contained in Giblett (1932) and later in Shiotani (19501. Cramer (1951). McCreadq (1953) and Sutton (1953). .4lthough man) of the measured distributions had some degree of positive or negative skew. there ivas no consistent bias either way. Measurements made b! Press (1957) indicated the validity of Gaussian distributions up to values of the standard det,iation: “moderate” however. at e.xtreme values. the measursmrnts varied from that predicted by the Gaussian distribution. In the period ISS@l959 the available data applied to rural terrain. and it had to be assumsd that urban distributions are similar. The theoretical work of Novikoi and Stewart (1964) suggested that the probability distributions may vary irom the normal form. but no data wsre given in support of this. However. msasurements presented by Singer (1964) and Davsnport (1967) confirmed that the distributions i+ere normal or Gaussian. Finally. Blackadar. Dutton. Panofsky and Chaplin ( I9691 proposed normal distributions for measurements in the range &3ri: for greater (3 the) sugsestcd that there was a tsndsnc! for a higher proportion of larger gusts than indicated by the Gaussian distribution. The above conclusions are generally supported b> other data a\ailablc from this period. TiI V/UWKW~TL,: the range In 536. a normal distribution is satisfactory: above + -3~ there is some evidence that this distribution is not applicable.


atmospheric boerA:>







Fig. -. Drfinitlon

of main




The major characteristics. of adiabatic boundar! lavers can be defined from the data of the I YSO-1959 period. The four main terrain t>pes defined in Fig. 7 are; Terrain t!ps I. Smooth 3. !vIoderately
Rough 4. L’rr) rough rough

to adiabatic atmospheric conditions. as discussed in Section I. have been included. In all cases the free stream vslocit! is assumed to be reached at 600 m.



show. sea Short grass. grass,crops. rural RuralYwoods. woods. suburbs L’rban.

Ice. mud.

The s\tsnsive data obtained by the end of 1972 has enabled the properties of the above. and intermediate. terrain types to be defined vvith some precision. In the data finally presented. some attempt has been made to make some allowances for errors such as: adiabatic conditions not completeI> established. or changing. during any particular test: measurements affected bq local topography or buildings: insufficient fetch for equilibrium flow to be established. The quantities considered in the following test have been presented as functions of the roughness length and all of the data which Were considered to apply

All of the known available data art prssentcd in Fig. ?: tht iour terrain types are indicated on the roughn<js length scale. \\‘hers possible. a method of analvsing msan velocity data was carried out which was intended to minimize the effects of doubtful data: this consisted of estimating power indices from each pair oi velocit! readings. at consecutive heights. from an! site. .A mean povvsr inds\: was then estimated. Hovv:v:r. in some‘ cases somt degree of over-estimation could not be avoided. It can be seen from Fig. S that the scatter is such. that ixorrect trends could easily be deduced if insuE&nt data are considered. The amount of scatter tends to increase with increase of the roughness length. This is to be expected. since these data. in addition to other errors, will be more subject to errors arising from insufficient fetch being available for sclrilibrium Bow to be established. for these

CURVE A 04 B C 0 0, E



0 001







1 00




IO 0



Fig. 8. l’ariation

of the pou-sr






.I. cot \IIHA>

reasons. a regression analvsis has not been applied here or to the data of the Wfollowing figures. The proposed variation of the power index with the roughness length is not a mean curve through the data but has been offset downwards since most of the sources of error tend to produce over-estimates of the power indes. The amount of offset was partially based on those data which were considered to be the most accurate and reliable. These data were used as a guide in producing the proposed curve; the data presented in other figures were treated similarly. Clearly. an analysis of this form is subjective to some extent; therefore the proposed variation of the povver index with the roughness length (Fig. 8) is the authors interpretation of the most accurate representation of all the data. The dotted lines are probable upper and lower scatter limits; data falling outside these lines can be considered as unreliable. Other proposals for the variation of the power index aith the surface roughness can now be considered and are shown plotted also on Fig. 8. It can be seen that the curve proposed here falls behveen the two more recent curves. i.e. from Helliwell (1970) and E.S.D.U. (1972). for terrain types I and 2 and for part of terrain type 3. Generally the E.S.D.U. curve falls near the upper scatter band limit and. like all the remaining curves. over-estimates the power indices relative to the curve proposed here. In general. it can be concluded that for roughness lengths greater than CA.0.10 m. the curves suggested by other authors lie outside the upper scatter band of the data and are therefore not considered to be satisfactory. Therefore, the variation of the power index with the roughness length suggested here is considered to be the most reliable.

at this height should be free irom ver! local intluences but still be representative of the local terrain. The height of IO m commoni! adopted for meteorological reference measurements is thought to be too low for man! sites. For sstremel! rough conditions s\sn n height of 30m may still bc too IoM.. but is to be regarded as a reasonable compromise. The scatter of these data ts considerably less than that of the mean velocit> measurements: therefore. this may be the best quantity to measure at a site and to us2 as a reference quantity in determining the other flow characteristics. Hovvever. the most important point to be noted here. is that the variation of the power inde\: and the turbulence intensit) with roughness length follow the same lavv. Therefore. if the value of a site power index is knon-n. then the magnitude of the turbulence intsnsit! 2t the site. at a height of 30 m. is also knovvn. The estimated variation of turbulence intsnsitk as a function of roughness length is also shown in Fig. 9. This was derived from. , (if -),li = -.



’ I or = 2.5 k ___ . i\ log. : 1,) !

and it can be seen that this expression over-estimates the turbulence intensity for roughness I:ngths greater than about 0.10 m. The above slpression was derived on the basis that. , (II -) C., - 2.5. i.e. ,-I = T.5. Therefore. the data of Fig. 9 suggest that ,-i should be reduced as the roughness length is increased: this reduction becoming significant for terrain types 3 and 4. If the roughness length is in this range. then an estimate of the modified value of .-I can be deduced from the two curves in Fig. 9. Although more data are needed for terrain types 3 and 4. the proposed variation of the turbulence intensity as a function of roughness length is suggested to be the most representative available.

All of the available data on these measurements are presented in Fig. 9. The reference height of 30 m was chosen on the basis that measurements made





= I/la:








ESTIMATE1 )‘iiij 1

w * z r 02 -

1 1 z z 0. I I 0.01 / /,,I, ,1,1,, I' 1 1 II 0.001 ,,I,,I ! 0.10

/ G-’




/ I






Fig. 9 Variation

of turbulence


with roughness



a~nilable data on Reynolds stresses are as 3 function of roughness length in Fig

under-cztimatc the Reynolds strews for terrain t!pc _. For stmplicitq. one could thcrsfor~ USC the ’ rclations:

I ii. In cornp~~rison to the other quantities considered. the availabk Reynolds stress measurements ar? relati\el> fen- and. as can be seen. are subject to considerable scatter. Some of the scatter is no doubt due to the inhswnt diHiculti<s in measuring the Reynolds stresses. caused. for esampie. by instrument rni~~l~~nrnent and bad siting. It is again etident that incorrect trends can be deduced hq’ being selective or restrictice regarding the measurements considered. .Although the data of Fig. IO have been represented h> a straight line. this representation is possibly open IU doubt (see Section .?A). especially for roughness lengths greater than about I m where the data are scarce and not particularly reliable. As in the case of the data previously presented. the more reliable stress measurements have been used as a guide in determining the curve best fitted to the data. Other forms for the Lariation of the Reynolds stress lsith roughness lsngh have been given by Davenport I196-4) and Pasquill (1970) and are also shown on Fig 11). Since these these curves are biased towards thz loww range of the stress measurements they do not appear to be representative of all the available data. Thw is also no apparent reason uhq the stress. presented in this form. should decrease at high roushnsss lengths as suggested by Davenport (1964. Thus is a ver) obvious need for more measurements particularI> in the case of terrain t)pss 3 and 4. In the meantime. the proposed variation as shou-n in Fig. IO. is suggested as a possible compromise (see Section 3.-i). 3.4 Conhitwti ii&r
Off the pow” irules. rd?Liluw

For arbitrar! values of z,, . SLICK as z;, 1;;. etc. the abo\s espression gives. -,lm) 2, _” -:, -“’ -,I etc. I % 0.12 076 .. (\ (Z, Ii)),)“, (II.i\ i*;)lo: O-12 0.26 0.12 0.36

The available data on the length scale. Lxx. are presented in Fig. I I. which shoxvs its Lariation \vith height (> l@m, and roughness length. Below a height of ccl. _%lOm it can be assumed that LIP, ivill decrease more rapidI> with decrease of height. due to the


iiirrv.\ir I‘ irid Rc~~w/t/.~ .wLwc5

Figures S and 9 shou that the variation of the poww index and the turbulence intensit! with roughness length follow the same law. The data of Fio ICI could also be represented by the same law = within the scatter band of the data. but will tend to

:QOQ _


1 r










= 1Q8(l/zol”6

Fig. 12. L’ariation

of length

scale with



and hsight.

of the ground. Figure I3 in which hf., at the reference height of 30 m, is plotted as a function of the roughness Isngth. may be compared tvith Figs. s- 10. Figurs 1I shows that the measurements are subject to much scatter. The positions of the lines. for various ~.alues of the roughness lengths. were again based on the data that were considered to be most a-&rate and reliable. It was assumed that these lines should tend to converge at some height. and that above this of terrain height LU would be indepsndent roughness. ‘This height was assumed to be in the region where the intrrrnittency factor begins to decrease in calus from unity; this is of the order of 140 m for a boundary IaFer of height 600 m. This also agrees with the suggestion in the literature that LUG should increase with increase of height up to 7OG300 m and is reasonably well supportsd by the in Fig. I I. The few measurements shown measurements above 240 m agree with flat-plate data which indicate that the turbulence length scale should

then decrease ivith further increase of height. this is assumed to be caused by the intermittency. It was noted in the previous section that Lu, was regarded. in some literature. as being independent of terrain roughness; this is not shown to be supported here. In addition. it was seen that the empirical theories of Davenport and Harris predicted that LL~, should increase both as the roughness increased and as the height continuously increased: the reviewed data shows that these predictions are not acceptable. If the height range IC-210 m is considered. then the length scale at any height in this range. and for any roughness length. can be derived simply from. Lll, = C($ ”

The values of C and I./K for any particular roughness length. can be obtained from Fig. 13. It is concluded that the variations of Lu, with roughness length and height deduced here are the most consistent and reliable based on the available data. despite the lack of agreement with previous predictions. With regard to the length scales Lu, and Lu,. it has been sholvn that these can be derived from a knowledge of Llr,. The remaining length scale of importance, Lit.,. and its variation with height has been adequatei! established by other authors. Several equations have been derived which can represent all of the data considered in the previous sections. the process of obtaining a boundary layer structure from these and other equations is summarised in Appendix I,


Fi:. I; Variatron _.

of C and 1,‘~ with



It has been shown in the reviewed literature. that adequate expressions have besn derived by other authors for the forms of the longitudinal and vertical spectra of the fluctuating velocities. In addition. since hr, can now be defined for any terrain type. the position of the peak wavelength can be fivsd on the


atmospheric boundar? la)ers
The variation the constant oi the longitudinal shear stress layer: turbulence tntenstttes


frtquenc\ accurac> as stated spectral considered from of scatter.

scak. to date this represents to which in the at shapes spectra reviewed low literature. defined.

the degree of However. detailed not be the should

can be defined. frequencies

as being accurately

since the data degree

the various

sites are subject

to a large


-t = 2.5 for 0.01 < z0 IN < @IO

and 2.5 > .-I > 1.60 for O.IOO < :,,nr < j-00. For IO0 < z(m) < 6W assume a turbulence intensit) of about @Ol at 6OOm. and extrapolate to this value from the top of the constant shear stress laher. The Reynolds stress in the constant stress lahsr:

-I. coYcL~sIoss
(a) \‘arious

anomalies literature

have been found on both and on the

to exist theoretical

in of

the published

the interpretation

measurements anomalies

= 2.75 x IO-‘+ The length scale of turbulence,

6 x IO-‘log,,,:,,.


predictions definition intensities variation terrain the

of some boundary of both the power terrain

layer characteristics. respect to the and turbulence
LU I = IOY(‘;‘:,)’ or as a function of height I&, from, = C (I)’ ” Ii) b. (6) Lrr,. at a height of 30 m:

(b) The major

occur with indices and with

for rougher of the length

respect to the of of
for. IO < r(m)

scale. LIP,, as a function show that the main simply for any boundary value

type. data length layer
< 310.

(c) The analbsed roughness characteristics

can be derived

from two figures

and where. The length

C and

VII are obtained




and one equation.
~c~Jro~~/l,t/yerlll,Jlr.s-Thc uork was carried out at the Central Electricit) Research Laboratories and the paper is published b> permission of the Central Electricity Generating Board. .Acknouledgemcnts are also due to Dr D. J. Moore for considerable assistance the final version of this paper. in preparation of

scales Lu, and LUG: I‘ll, = @3 _ 04 L1r,







: 19)

L”? = LA, = LA, 3
.APPEhDIS 1 is represented mean velocity. in the constant The power (H here ‘tl’ is neglected for terrain types I and 2). The msan velocity power index and the turbulence tntsnsit> : for 710 < r(m) G 600. The length scale Lw,: LLL., = 040 :. sheer stress layer. and co-spectrum densIt> forms:


Thts adiabatic houndarq layer structure the following equations. Roughness length can be derived from. measurements for 1.5/t, < :(m) < 100;

t 10)


where. .U = ~Y’ri,,,. Y = IS00 m = I.075(~jjtn),,*1
I i I3(j“/m)' 3'

Ks,(lI) = O.O96log,,:, (applicable The lateral for OGlIl i @016(log,,~,)’ + 0.24. where. fm or 0.32


g z,, 11, < 5.0 III). turbulence intensities;

and vertical

where. ~;JI 2 -0.08

Source Stevenson (IYSO)

Site Open terrain Cereal Farnborough Ball) bunion Salisbury Plain Leafield Cardington

I1 0.143 0.166 0.33 @I30 0.I :+o. I43 0.17 0. I ‘Y-0. I13 @I30

-,,lm) 04014 0.04 0.0 I I O-OI 0.60 o-o

Dines ( I9 I?- 19 I-3) \\‘ing (1921) Scrase (1930) He>wood ( I93 I ) Giblctt (1932) Best (1935)

I Colrrilllrcd



0.113 0.113 0.15 @22 040 0.20s 0.23 0.122 0.093 0105 0. I 6-o.I : 0.3; 0,236 003 I 0.17 0.73-0.35 0.36 0.1 I 0. I 52 0.12 0.08 0.16 0.21 0.32 0. I 6-O.



( 1946)
Cardington Akron Tokyo Quickborn Leipzig Sea ,Ann .Arbor Sea + Islands Cardington Sale Tokyo Sea + Land Caspian Sea ONeill O’Neill Brookhaven Copenhagen Hojer Frerslau Hanford Harwell Idaho Brookhaven Leningrad O’Neill CardingtonSale Cardington New York Leipzig Brookhaven New Orleans Washington Water Moscow Round Hill Downlands CSNeill Open Sea Sendai Airfield. Cardington Tokyo Porton Tokyo Suburbs Rural. Flat ONeill Tokyo Coast Round Hill Brookhaven Tokyo Cedar Hill Tokyo Round Hill Cardington Sale Hanford London (Ont.1 Minneapolis Louisville Hanford Sea St. Louis Montreal Hanford Librral

0.0 I
0.026 0.0 I

Frost I 1917~ Huss and Portman (IWS) Shiotant (i9-H) Franck2nbergrr (1919) Lettat (1950) Shsppard (195’) Hat (19551 > Sherlock (195.3) Juul (19511 Rtdrr (1954) Deacon (1953) Kamci (1955) ‘.Vau(1956) Goptarsv (1957) Lettau (1957) Pa”ol‘~k\ (1957) Jensen (19581

De Marrais


Smger 11959) -\r~el L’I nl. (I 960) Blackadar cf al. (19601 Takcuchi (1961) > Durst (1960) Davenport ( 1960)



and Hudson


0.176 0, I19 0.39 0.33 0.3 0.384 0.2.3g 0.1 I4 0.303

Ibanov (1961) Pasquill (1961) Taksuchl Deacon Londo (1961)

0, I 6-0. I 7

( 1962) ( 1962)

Saito er nl. (I 961) Pasauill (19621 Shiotani i 1963) Bb7ova (1963) Panofsky (I 963) Kawanabe (I 964) Lumley and Panofsk! (196-l) Slngcr (1961) Soma (196-t) Thullisr and Lappa (1964) Yamomoto and Shimanuki (1964) Berman (1965)


0.25 0.30 0. I b0. I 7
0.35 0.1 17

0.01’5 OOOS
-J:- _>-


0.22 0.302 0.143 0.302
0.149 0. I 76 0.1’ 0.36 @?I 0.26 0. I 1 0.10 0.X 0.28 0.13

I .o ,.‘T _ .>_ 0.03 I .-IS I ,Yj
0. I COG4

0.0 I

Blackadar (1965) Davenport (1965) Dcland and Binkowski Elderkin (19661 Kraus (1966) DaLenport (1967) Eldsrkin (1967)







Fixzola (1967) Paulson I 1967) Shcilard (1967) Shiotani 11967) Volkovitska>a and ivanov Harris (I9681 Jones t’r al. (19681 Munn (1968) Blackadar (jr al. (1969) Fichtl and McVehii (1969) Pasquill i 1969) Slade (1969) Colmsr (1971) Dutton (1971) Harris II971 I Harris (1971)

Site Brookhaven Sea Mend&ham %a


z., (ml

i 1967)
Rugby Liverpool New ‘r’ork White Sands Kenned!. SC. Urban ~hiIad~lphia RAE. (Bedford) Kenned) SC. Rugby Cranficld Rugb) Suburbs

Where sufficient data are not available from which to interpolate the value of the turbulence intensity at a height of .:O m. the followtng method of estimation is used. The data of Shiotani (1953) are used as an example since sutftcient informatiol~ is given from which a value of turbulence intensity can bc interpolated graphically, and hence the estimated values checked. _. Sate: Snow covered -(m) 7.5 IL 75 la) I = _;; \ (II _)!‘ir

(b) : = 7.5 m

,I&=----log, .‘_ 0.156 0.1’0 0.063 Mean [,


I30‘0.00 ‘I I




values from (a) and (b) are: [, C&&,> “, = 0,103: :(, = 04)OlYm. of turbulence intensity at



(c) Graphical 3 = 30 m gives:


log,. :
-0 Giving

= s.34. !VOfi,
r. = 09026 m



ii],, “, I= O,Ioo - 0~105

In the following tabulated data (5) either indicates: 2, estimated from given turbulence data or [, (F),ti],,, estimated from a given roughness length, The range of roughness lengths over which such estimates are consrdered to apply is discussed in the main text. The other values of turbulence intensity at I = .;O m have been obtained by either interpolation or a moderate degree of extrapolation of available msasurrmznts.

at 3 = 30 ml

Source Best (1935) Shiotani (19-8) Cramer (1952) Sheppard ( 1952) McCready (19 j3) Shiotani (1953) Lettau and Davidson (1957) Dursr ( J960) Davenport (1961) Ivanov and Klinov (1961 J Pasquill (1961)

Site Rural snow (‘T) Shrubs etc. Water Trees. etc. Snow Rural. flat Rural. flat Rural. Rat Urban Downland



zolml MI O-WI(E) 0.0_‘6 (E) O.I:O(E) O-00 I 0.05(E) tIM119(E) O.#iT @0065 0~02 3W 0.01

@lOY 04297 0.112 (mean) 0.I Y1 (max.) O.I’:!

0.103 o-l34 0.128 @l-t5 0.275 @15(E)

Pasqulll (19621 Shiotanl (19621 B>zo\a (I9631 LJu-anahs (13Mj Lumle! and Panofsky (196-J) Singer ( 1964) Soma ( I Y6JI 1’amamoto and Shimanuki (1964) Su-anson and Cramer (I9651 Eldcrkin (19661 Davenport and Is)umo\ 11967) Shsllard (1967) Shlorani and .Arai (1967) Graham (1968) Harw ( 1968) Kaimal and Haugen (19691 Slade I 1969) Calmer ( I971 I Harris ( 1971) Harris I 1972)

Air&Id Rural Hat Rural Hat Rural. flat Suburbs Rural. flat L’rban Coast Woods Woods Urban Urban Brush. sand dunes Rural. Hat Woods Rural Coast Urban Rural Rural Urban Rural Rural Rural. Hat

0.1 IUE) 0.1 IS(E) o- I I q E ) 0.122(E) 0,2?‘(E, 0.1-1 O.<YI(E) @152(E) 0.2-10 0235 0.30,39E, ().:-IS(E) 0.70 @II 0.27

@17(E) 0.30 0.17 0. I 75 0~131


Source Taylor (1916) Scrase ( 1930) Sheppard ( 1947) Pasquill (1950) Shlotani (1950) Sheppard (I 952) Sheppard and Omar Deacon (1953)

Site Rural. Hat Grassland Rural Grass Grass. vegetation Sea Water Grass Water Rural Rural. flat Rural Rural Rural. flat Sea Sea Rural. Hat Woods. Urban Rural Rural Woods Rural Urban Rural Sea Woods Sea Sea Sea Sea Sea

oal I10~00~0
0~001j_0~0017 @CO30 (mean) OOOIO ONQ-1 OIX~ I I

-,dml @OIlassumed) 0.01 0.05 I mean) 0.0()66 0,035 0Ixl I O~COI~assumed) 0.015 oJ2l IO


@oooJ oGQ2 I
OooO6 OOOI!j OQOO83 0.001: 0.0022 OQOl7 OOOiI5 OOCO5 OQOl7 OX!O32 ON2 O~OOlJ5 0.003 OQO25 OOOl2 0@116 O+UIl65 O+NQ36 OQO25 O.OCiI6 O.o00.;5 ON)052 0.003 O~OOO4Y

Ha! (19%) Monin and Obukhov (195-1) Rider ( 1954) EllIson (1956) Deacon (1957) Lettau and DavIdson (1957) L’inogradova (1959) Deacon ( 1962) Bhzoba (I963 Siryr (I 964) Soma ( 1964) Thullier and Lappe (1964, Berman (1965) Blackadar t’r al. (1965) Davenport (1965) Elderkin (1966) Kraus (1966) Fri7zola cr al. (1967) Paulson (19671 Smith (1967) Keilcr and Burling (1967) Gibson and L\‘illiams (1969) Hasse er a/. (I 969)


0.01 I

0.01: I 011 7.33 -_0.0.: 0.0; I .oo 0.0’ 7.17 - _ 0.025 03txl I I .O O.UIO6





Taylor (1915) Giblstt (1932) Shiotani (1948) Shiotani (IUSO) Cramer (1952) Priestlq (1957) Sheppard i 195’) \lcCready (1953) Robinson (1951) Shiotani (1953) Tablor (1955, \Vebb (1955) Ha! and Pasquill (1959) Davenport (196la)

Rural Rural. Hat Rural Grass. vegetation Trees. bushes Rural U’atrr Rural Rural Snow Rural Rural Downland Rural. Rat Woods


I~anob and Klinov



Pa%Jtlill (1961)



C 1961)

Rural Urban .:O 26

Soma (I Y6-Q

107 I73 33 7 ; I2 15 16 23 30 46 64 91 16 64 I5 16 46 .; 6.1 76 3 6.1 3 6.1 1: ;b 9’ 10


( 1965)

Various sites

Woods Rural. flat Rural Eldrrkin (1966) Rural Urban Rural

Davenport f 1967) Elderkin (1967)


t’r al. (1967)


Shiotani (1967)





i’r ai.




f 1967)


Smith f 1967) i’oiko\itska)a

and I\ano\

I 1967)

Sea Rural(“)

Busch and Panofskt


Grass K’oods Rural Sea

Harris I1965 t Fichtl and McVehil

i 19691

Rural Shrubs.


Gunter .-\ntonia

(1969) and Luxton


w T. Tests


( I97 I 1











I <s: 30 ‘50 -_

The follo\ving References are in chronological art: in alphabetical order for each qcar. REFERESCES



Van E\erlnpdon kels Zul-ichcn 75.

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Stevenson T. (I YYO) Rsport on the simultaneous obssrvations of thz force of the \vind at different heights abovr the yound. J. Scar. wr. Sot. 5. 3lS&?jl. Guldberg C. M. and Mohn H. (1883) Srfrtlics ~/‘r/rtj :Llor<,~twr.s o/. r/w .-Irmo.sphw. (Translated by Clr~sland) .Abbs-Smithsonian Miscel. Collection 1910. Archibald \V. (ISSjl An account of some prsliminar! experiments \~~th Birams anemometers. attached to kite striny. .~~~rwr. 31. 66. Ekman \‘. \\‘. (1905) On the intlucnce of the Earths rotation on ocean currents. .Arkir. mrcir~t7riX. mw0170fi1i

Shau ii’. N. (IYIN) Details of wind structuw -\d\isorq Committee for .&ronautics. R. & M.. Ko. 9. Dines J. S. (19131 Structure of the wind. 3rd Report to the .-\dvisor> Corn. for ,Aeronautics. R S: M 47. Dints I\\‘. H. (1913] The vertical distribution of Tsmpcrature in ths atmosphere and the work required to alter it. Q. J. R. 1!7~‘t. Sot. 29. IS5-192. Rawson H. E. ( 191.:) ,Atmospheric bales. eddies and vor[Ices. .-lrwmr~~rJ. Ii’. 2455256. Dobson G. &LL.8. I lYl-1) Pilot balloon ascents at th? central Hying school. L’pavon during the !car 1~13. Q. J. K. IllC’i. sot. -lo I ?.:-I 35, Shaw \\.. N. (19141 Wind gusts and the structure of aerial disturbances. .4cwmrur J. 18. l7?-203. Taylor G. I. (19151 Eddy motion m the atmosphere. P/I;/. TWIIS. R. SW. 215. l-36.


.Akerblow F. (190s) Rechsrchss sur Ies courants les plus has de l’atmosphcrs au-dcsus de Paris. .Voc. .-lcrtz Scb~irr. (L~pstrh) 2 Ser. 4. So. 2.

Ieric boundar! T,~!lor G I. I 19161 Skin frlctlon of the wind on the Earth’s on the

laqers on the variation of ~lnd with

surixe. P rr>~’ Ro). SOL.. 4. 92, Scar‘-1. Taylor G. I. j I\)171 Observations and speculations nature of turbulent SJI. Corn. for Xero.

Sutton 0. G. (1931) Notes hrlght. Q. J. R. r~wt Sm. Durst 36 of wind ober dit%rent

33. X%33

C. S. (1933) Notes on the variations sur&~s. Q. j.

the structure

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R. mt’r.




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Pettcrsen T. .md Suinbank IV. C. (1947) On

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H. 119501 .-\ re-examination of the Leipzig profile considering some relations between YI ind turbulence in the frictional laber. ~&.s 2. 125-

I 19471

I’ertical Proc.

of heat bk turbulrnce

in the atmosphere.

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-\diahatic Sre\\art H. J. and \LcCrzsd> P. B. t IY~ZI pherlc turbulenw C.I.T. Contract So. U.S %‘tather Bureau T.l!lor R. J. 1195?1 The dissipation of the lo\reit la>crs of the atmosphere. Q. l-Y-Is.5



la)erj oi the atmosphcrlc a \vatcr wmd suriace. Q

Report on JtmosCHb.-3115 with kinetic encrgq in J. R. ~rwr. Sot. 78.

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./or .Appl. .\fKll.
at the Rqnolds stresses.

Stewart R. W. (1956) ;\ new look Cw. J. P/IJS. 3-l. 722-725. Blackadar A. K. (1957) Boundary their significance for the gou-th Bull. +,I. wt. Sot. 283-290.

Layer wind maxima and of nocturnal inversions.

Charnock H. and RobInson G D.

J Cor hIHA\

(1’9571 Spectral


from subdlbided metreorologlial series. .Alr Minijtrh 41e:t. Res. Corn. 41.R P. So. 1062. Corrsin S. 1IY5’l Some curr;‘nt problem5 in rurbulent shear tlous Chap. 15.. Sakal Hkdromcchanics Publ. 515. hat. -\rJd SCI.. \.R.C. Cramer H. E. (195-1 A pracrical method ior csttmatlng the dtspersctl of atmospheric contaminants. Proc. Iif. .Vc~r. Co/!). 4ppl. .Ift,r.. Harriord. Connecticut. Deacon E. L. (l9T71 I\ ind profiles and the shearing strcjsan anomal) rcsol\ed. 0. J. R. ~cf. Sot. 83. S37-j-IO. Deland R. J. and Panoisky H. -\. (I9571 Structure of turbulcncc at O’Ne~ll %brasLa and its relation to the structure at Brookhaien. Sci. R:p. 2. Contract No. ;\.F. Is, 6W-1017. Halstcad XI. H.. Richman R. L.. Cove) I\‘. and Merryman J. .A. (1357) ,A prellminar) report on the design of a computer for micrometsorolog2. J. .1/~,f. 14. 3OS. Jones R. .A. (19571 Studies of sddk structure in the first few thousand feetoftheatmospherr-a prrliminar) c\amination of rhe spectrum and scale of the vc’r[xal component at 3COO ft. k1.R.P. IWI. S.C. II I 231 (Porton Tech. Paper MI Jones J. 1. P. and Butler H. E. ( lY3-i) Studies of eddy stl-ucture in rhe first ic\k thousand feet 01‘ the stmosphcremcasuremr‘nt of th? vertical and horizontal components. M.R.P. IO:S. S. C. I I 1’229. Lcttau H. and Dat idson B. I 1957) E \-/~/or~fry I/I<> E~fi1.3 .4rn1o.~~Av1~. I YI .!f~/~,. Vols. Pergamon 2 Press. Oxford. Uotess C. B. (lY57) \ jtud! oi rhe nature of atmospheric turbulence based on [light measurements of the rust \elocit) components. \\‘.-\.D.C. Ttch. Rep. 57 356 -\STI-\ Dot. So. -\DI Ib3-l: L.S..-\.F. Press H. (1957) Atmospheric turbulent cnbironmcnt \+ith spcclfic reference to continuous turbulcncc. R?p. 115. -\.G..A.R.D. N..A.T.O. (Paris). Tallor R. J. (1957) Space and tlmc correlations in aind velocit\. J. Md. 1-l. 37% Townsenh A. .A. (19571 The turbulent boundary lay. Pwc. f,L’.T..4..\f. SL’UI. 011 Bowtl. Ltrwr Rrs.. Springer. Berlin. \ an der Hoben 1. (1957) Po\\ir spectrcim ol‘ horizontal uind speed in the frequcnc! range from QOOO7 10 900 cb, hr. J. .Ifc,r. 14. 160. Barad Xl. L. (Editor] I 1958) Proj~t Prtririr Grass. h Field Programme in DitTuslon L’ol. 1. II. Bullen XL’. 1. (19%) The distribution of gusts in the atmosphere; an integration of L’.K. and L’S, data. A.R.C.. C.P. No. 119. Elliott A‘. P. (19%) The growth of the atmospheric internal boundar) lajer. ?ix~\. .~uI. Gro/~h.s. IIIWI 39. IO-W

The rAtIon 0. .I R. i,,ci. DcTlcon E. L.





space spectra. tl-an&r

Sc>c~. 8(.

measurement of rarbulent

( I9591 The

in the lo\\er atmosphere. 4ci1.. &o/>i~i,). 6. 21 l-22-1. De Xlarrals C. A. \b’ind speed profiles ,tt Brookhaven \atlonal Laborutorb J. .!I, I 16. lyl- 130 Franczshml G. -\ (IYS?, Xlxromcteorologlcal obser\ations oter non-idcal surt:,Iccs. Sa. Rep I. Conr. -\.F. IY 160-l)1150. Texas .A & XI College. Gitrord F. (1959) The Inrerpretation of metcorologicn~ spectra and correlations. J. .\fc,r. 16. AU .3-16. Hab J. S. and Pajquill F. I 19591 Difuslon from a continuous sounx in relation to spectrum and scctk of turbulence. .-ltl~,. &o:+..s. 6. 345 365. Henri R. M. (19SV) stud! of the etlects of LLmd speed. .-\ lapie rate and altitude 04 tb.e spectrum of atmospheric turbulence at loa altitude. I..-\.5 Rep. 53 43. Johnson 0. IlYS9j -In c\amination OT the v?rticnl wind profile in the lo\\<st Inhers of the atmosphere. J. Afar. i6. I-l-c- 1-M. Jones J. I. P. and Pusquill F (19591 An c\perimentai sqstern for directI) rxordino statistics oi the intensitv of atmospheric tu&ulence. 6. J. R. im’r. 5~~. 85. 2X-736. Lettau H. (1959,) \\‘ind profile. surf&e s[r:js and :costrosurface layer. phic drag coeticicnt in the .~tmospheric .4,/r. Gvopl~~. 6. 2-11-157. Lettau H. (1959b) Studies of the .;-D slructur? of the planetar! bounder! layer. .Ann. Rep. D..~.-~h-019-~C-S01S’ U.S. Army Elcc. proovlng ground Notcss C. B. (1959) -\nalqsis of turhulcnce data measured in flight at altitudes up to I600 ft. nh~\e three different types of terrain. Cornell Aero. Rep. T.E.-I 215-F-I. Panofsk) H. -\. and Deland R. J. I 19591 I-D spectra of turbulence in the lowest IOOm. .4tlr. G++~s. 6. 41-62. Panoisk) H. .A. and McCormick R. .A. 11919) The spcctrum of vertical \clocitx near the sul-face. I..A.S. Report. No. 59 6. PriestIe! C. H. B. (1959) T&Av~r Tr~!slir ~JI tin Lotrrsr .-Iruroiphw. Cniiersitl of Chicago Press. Chicago. PriestIe! C. H. B. I 1959) Esnmation of s:!rt’lcc stress and heat tluv from protile data. 0. J. R. mr. Soz 85. JI5--&IS. Robinson G. D. (lY5Y) Vertical motion and the transfer of heat and momc’ntum near the ground. 4tlt. G<,oph~.s. 6. 7% 268. Singer 1. -\. and Ra!nor G. S. (1959) ;\ stud) of the wind profile In the louest 400 ft. of the armospherc. Prog. Rep. 1. Brookhaven National Lab. Vlnogrado\a 0. P. (1959) Tangential wind stress above a disturbed sea surblcc Bull. 40/t/. Sci. I S.S.R. Gcoph~x SC,. II (Trans. b> .-\m. Geophi. L nion). Yamamoto G. (1959) Theorq of turbulent transfer in nonneutral conditions. J. .\fl,r. Svc. ./up. 37. 6(>~69. Stewart R. !V. (I 951)) The natul-al occurr:nc: of turbulence. J. qcopl~~~. Rc,.s. 6-i. 2 I I Z--J Ii I Aricl S. A. and Kliuchniko\a L. .A. (IS&I) Wind over a Cit). (Vetcr Vuslo\unkhgaroda) L.S.S.R. Gla\ naie. Geofiz. Obserb. in A. I. Valiko\a: Trud) v>pusk. 9-I pp. 29-32. Blackadar .A. K. i 19601 .A sur\cb of uind charactct-ljtlcs below IX0 ft. .\fL,r. .Lfoiroy. A’j. Blackadar -\. K.. Panoisk) H. .A. !vIcl’ehil G. E. and Ii’ol&ton S. H. ~I9601 Final report on structure of turbulences and mean aind protiles wlthin rhe atmospheric boundark Ia)cr. Dept. of &let.. Penn. State C’niv. Cont. ivo. .-\Fl9(6M)-5231. Cramer H. E. (19601 Engineering estimates of the power spectra of the horizontal componcntj of rhe wind velocit!. .:rd ConI: of .App. &let.. Santa Barbara. Cramer H. E. (1960) Cse of po\ver spectra and scales of turbulcncc in estimating u ind loads. .\f(,r. .\fouog. 4. I?DaLcnport A. G (1960) Rationale for dererrnming design wind velocities. J. Srvuc. Dir. P,oc. .4.S.C.E. 86. 39. Durst C. S. (1960) U.ind speed o\er short periods of time. .\fc,r. .\/rrc/. 89. I YI.

I OjJ.
El\ R. P. (1958) Spectral .-\nallsls of rhe L-component

.yc~rl~r.cl/ CC;NI/. pp. I21 -I 28. Int. Edit:. Vol. 1. No. 4. Danish Technical Prsss. Copenhagen. Johnson 0. (1958) The relation between wind \elocit! at Xt.. -1Oft.. IO00 ft. and its dep<ndance on atmospheric stability. Ralston. -\lherta. Sutield Euper Stn. Tech. Paper I I6 Jones R. A. I 19%) Porton Tech. Paper. 635. Jones J. I. P. and Butler H. E. 11958) The measurement of gustin<ss in the tirst few thousand feet of the atmosphcrc. Q. J. K. 11i1’r.Sot. 84. Ii-24 Grant H. L. 11958) The large eddies of turbulent motion. J. F/u,d .lfcc/r. 4. I-19. blintz Y. (195s) .An empiricall) determined suriace stress coetliclcnt for numerical forecasting experiments. Proc. SIri! G,,u. 4s.~. in Toronto. Canada-Int. Ass. of Meteor. and .Atmos. Phbs. ILondon). P,lnofsk\ H. A. and Brier 1. (19id) Some upplicarlons of statistics to meteorology COIL of Mineral Industries. Penn. St. Lnic. Panofsk) H. .A.. Cramer H. E. and Rao 1;. R. K. I 19%)


Jtmosphr xic




of a turbulent !cloclt> field In the lamer ?011 m laher oi the atmosphere. Ix. Groph!_s. Srr. 13. 15’&-15‘7. Graham H. E. ,\nd Hudson G. \. (141601 Surface \hlnds n-ar the ccntx of hurricanes iand other ckclonesl. Xat. Hurricane Res. Pro!. Rtp. 39. Dept. of Comm. C.S.U .B. Islltzer N. F ( IY6UI &leteoroloycal parameters of ditTusion. DIK Climatolog> of the Satlonal Rractor Testing Stn.. 1 s. K‘tzanskii .A. B. and &lonln A S. I 19601 -\ turbulent regime above the ground dtmosphcric laker. /:t. G~v/~/I! 5. SL,I.. so. I. III-III. Panofsk! H. .A Blsckadar \. K. and Mcl’chii G. E. II9601 The diabatic ivtnd protilc. 0. J. R. wr. Sot. 86. 390. Panofsk! H. -\. and 4LcCormlck R. ,A. (19601 The spectrum oi vertical lcloclt> near the surface. 0. J. R. ~wr. SW. 86. -19% Saunders K. D. (1960) Interim report on the technical analysis of the B-668 IOU Ietel gust stud> Rep. No. SM5973.. Doug. .Aircraft Co. Ltd. Singer 1. .A. (I 960) .A stud! oi ths \\ md protile in the lowest 100 ft of the atmosphsre. Pro!. Rep. 5.. Brookhaven Sat. Lab. Taylor R. J. (1960) -\ new approach to measurement of turbulent tluws in the lower atmosphere. J. Fluid .\luch 10. 449%-I%. Taylor R. J. I 1960) Slmilarit! theory In the relation hctwecn Hu\cs and gradients in the lower atmosphere. 0. J. R. ml-r Sot. 86. 67-X Taylor R. J. f 19601 Form of \\ ind protile in the near @round la\er of the ntmosohere. 1:r. .-l<wl. SC;. L’2i.S.R. Groah~x s,:r. 12. ls:I-ls2i. c U.S. Public Health Service I 1960) 3rd ,Atr Pollution RLIS Seminar. Rep. 7% pp. 1173--i lS9. \\‘an-Chang Chiu (1960) The spectra of large scale turbulent transfer of momentum and heat. J. .LIt,r. 17.71;C -1-11. \Vilkins E. M. (I9601 Diwpation of ensrg! b> atmospheric turbulence. J. .\f~,r<o~. 17. Y 1-92. NIppermann F. U. and Klug M’. (19601 Schornsteinmmdesthohen lhrc Bestimmung atls Gesetzmassigkelten der turhulentr ditTusion in der .Atmospherc. L’.D.E. Zbrozek J. K. I lY60) The relattonship beween the discreet gust and pov\cr spectra presentation of atmorphcric turbulence x~th a sugsestrd model of ION altitude turbulence. R & 51. No. 3216. Zbrozsk J. K. and Ridland D. M. (1960) A measured po\bcr pheric spectrum turbulence of the vertical component R.,\.E. T.S. ,Aero 26SI. of atmosJLnscn hl. I 19611 Copenhagen. Lalhhtman D. L. thf :ttmosphsrc.






I 19611


Ph>stcs oi the boundsr! [Translat:d

la)cr oi bb I\I. . (

Prog. ior SC!. Trans I lY61).] \lcCol-mlck R. .A. (EdItor) (I9611 S\mposlum. -\lr o\i‘r cltxs. Tech. Rep. NO. -\62-5. C S. Pubiic Health Ser\tce. Connecticut. Panofsk) H. A. (1961) An alternative dcrl\ntlon of the dlabatlc wind profile. 0. J. R. rrwr. Sec. 87. IWI I I. Pasquill F. (I961 I The statistics of turbulence In the lower part of the atmosphere. Paper -1. Sbmp. on -\tmos. Turh and its Rslatton to .Aircraft. R..A.E. Farnborough. Rauner yu. L. (1961) On the heat budget of a deciduous forest in ninter /:r. fccltl. So. I’.S..S.R. G~oy. .>c,vic*_1. S?mYO. Saunders K. D. (1961) B-666 low lr\el gust stud!--Vol. I. W..A.D.C. Txh. Rep. 60-.:05 I\.right-Pat. .A F. Base. Ohio. Stuart R. IV. (1961) The wabs drag of wind o\i‘r water. J. F Illi‘/ .)I ?C/I. IO. IS’)- 194. Takcuchi K. ( 1961) On the structure of the turbulence ticid in the surface boundar) layer. J. mr SK Jifp. 39. X-167. Zbrozck J. K. (1961) ‘Aircraft R.A.E. Bedford. T.N. Iero. and atmospherx 3790. turbulence in the surface \‘oes. Nauch.

Zilitlnkevich S. S. ( lY6l) Turbulence rqions labt‘r of a transient air-stream. Trudy Meteor. Sovrsch. Leningrad 7. pp j-10.

Blackadar .A. K. (1962) The \ertlcal distrthurwn of uind and tul-bulcnt exchange in a neutral atmosphsr?. J. y,w /dn Rcs. 67. .;OYj_lO2. Chandler T. J. 11962) Londons urban climate &~y J. 127. ?79- 30’. Cramer H. E.. Record F. A. and Tillman J. E. (19611 Studtcs of the spectra of the vertical Ru\cs of momentum. heat and moisture in the atmospheric boundar! layer. Final Rep. D.A.. 3A9Y-27-005-0X. Cont. D.A.-.;6O3Y-SC-SO’W. blst. Dept. M.I.T. Crosslq A. F. 11962) Extremes of wind shear. &tet. Off. Sci. Paper 17. London. Deacon E. L. (1967) Aerodvnamic roqhness of the sea. J. Grophy~. RL’s. 67. 3 167-j 172. Deacon E. L. and IV&b E. K. (1962) Interchange of properties between ssa and air. C.S.I.R.O. !.lct. Phhs. No. I. GitTord F. A. (1963) The vertical variation of atmospheric eddy energ) dissipation. J. Mcrm. 19. ZO%?Oh. Gurvich A\. S. (lY63) Spectra of pulsations in the vertical wind velocity component and their relation to micrometeorological conditions. Trans. (Trudy) Inst. -\tm. Ph)s. Acad. Sci. U.S.S.R. No. -1. Hall J. C. (1962) -\ re-analysis of existing gust data using the Power Spxtrum method. De Havilland .Asro. Rep. 3287 (A.R.C. 24397). Johnson W. B. (1962) Seasonal and regional wiations of the atmospheric boundar! layr parameters and enew dissipation dsribed from Greg& serological survey of the U.S. MS. Thesis. Univ. of &‘isconsin. Klassen I\‘. (lY6’1 Xlicrometeorological ohserxations in the North Saskatchewan River Valley at Edmonton. Rep. No. Tee. 40% Met. Off: Toronto (CIR-3651). KolmogoroH .A X. (1962) .A refinement oi a previous hypothesis concerning the local structure of turbulence. J. F loid ,Ilr,ch. 13. S2-85. Kondo J. (1962) Observations on wind and temperature profiles near the ground. Sci. Rep. Tohuku Cniv. Szr. 5. Geophg. IA. pp. -11-56. Lettau H. (19621 Theoretical wind spirals in ths boundar! la!cr of a baroclinic atmosphere. Brir. Z. PilJsik. .-Imro.s. 3s. I95 212.

F. and Smith F. B. (1961) Statistics of lateral at I6 m above the gound. 0. J. R. mr. Sac. 561. (1961) \‘lscous dissipation in the atmosphere. J. .Cfcr. IS. 553-557. Businger J. A. 11961) On the relation bct%rcn ths spectrum of turbulence and the dlabatlc wind profile. J. qropir!x Res. 66. 2-W-2109. Cramer H. E.. Record F. .A.. TIllman J. E. and I’aughan H. C. (1961) Studies of the spectra of the vertical Husrs of momentum heat and moisture in the atmospheric boundaq la)er. -\nnual Rq. hl.1.T. Round Hill Field Stn. Dalr)mplc P. C. (I961 ) South pole micrometeorolog) programme. Tech. Rep. E.S.-2. Quartermaster Res. Centre. Sotick. Mass. DaLenport A. G. (196la) .Appllcation of statwlcal concepts to the windloading of structures. Pm-. /KC Cir.. EMJIT 19. 119~372. Dakenport .A. G (lY6lb) The spectrum of horwontal gusti. ness near the ground in high winds. 0. J. R. m’r. SOC 87. IYA--‘I I. De ,Varrais G. .A. II961 I \‘crtlcal tempsraturs diffusion observed over an urban area. &r/l. .-IvI. vwr. Sec. 11.

Abbott P. gustiness 87. 519~ Ball F. K.

Ixanov V. N. and Klinob F. Ya

I 1961)

Some charactsrlstlcs


J Cot. XIH.A\r -\ u~nd tunnel tn\estigatton oi ground ~tnd loads on

Lettau H. t 196’1 Studies of the 3-D structure‘ oi the planrtar) boundary laker Univ. ‘A’isconsm. Cont. D A.-X039-sC-wu’. i I XlcCready turbulence. >lcCrcady H. H.

a\\-symmetric launch \?hxlcs. S A.S.4. T\DlxY:. Burns .A. (I9631Power jpectm oflo~-lc~el turbulence sured from an atrcraft. R .A.E. T.\. Structures 32Y. Burns 4. ilY6.:1 Pobcr spectra 01‘ the vertical of atmosphertc turbulence ohtamed from


(1’962) Th?
J. ${~wyir!x



of atmojphertc by satI

Rrs. 67.

105 1059 Imeasurements

(1962) Turbulence

component concurrent

plane. J. yt@t.n. RCS. 67. I(Wl 1050. Montn ,A. S. (1’362) Empirical data on turbulence in the surface layer of the atmosphere. J. qwphp Rtjs. 67. 3 IO?21 I I. Monin ,A. S. (1962) Structure of fields of ~tnd velocity and temperature tn the atmosphertc boundary la!er near the ground Trudy .A. N. S.S.S.R. Inst. Piz. -\tmos. 1. pp c?O. Naito T.. Nasu Z.. Takeuchi .\I. and Kubota G. (IY61) Construction and vibrational characteristics of the Tokyo Towr. Bull. Sci. Eng. Lab. Wascda L’ni\. Vol. 19. Obukhov ,A. IM. (lY62) Somr special features oi atmospheric turbulence. J. y~wph~~.s. Rcs. 67. 301 I --301-1. Panofsky H. .A. I 1962) The budget of turbulent energy in the lowest IO0 m. J. yrop/r.tx RCT. 67. 3 I6 I-3 166. Panofsky H. .A. (1963) Scale analysis of atmospheric turbulence at 2 m. 0. J. R. trier. Sot. 88. 57-69. Pasquill F. (1963) -Ir~to.rp/rcric D~fiiwo~r. \‘an Nostrand. Sew Jersey. Pasquill F. (1962) Recent broad band spectral measurements of turbulence in the lower atmosphere. J. ‘/caplr!% Rr.7. . 30’5-303. 67 _ Rsiter E. R. (1967) The atmospheric micro-structur? and its bearing on C..A.T. Color. St. L’ntv. ,Atmos. Et. Tech Rea. No.-39. N.\\‘.R.F. 1%1062-069. N,AS.A-$6.:-IOJYY. ,A I5289 350. Singer I. A. and haglr C. M. (1962) A study of the wind profile in the lowest -100 ft of the atmospheR: Final Rep. Brookhaten Nat. Lab.. .-\ssoc. L’niv. Inc. S.Y. Shiotani M. (1962) The rslationship bctueen w tnd profiles and stabilities of the air layer in the outskirts of the tit). J. .Wc,r. Sot. Jtrp. Scr II. 10. 3 I j-:29. Swanson R. X;. and Hoidale M. M. I lY62) LOW level wtnd profile prediction techniques. Prog. Rep. -1. L’S Army Signal Misstls Supp. Agency. M:hitc Sands Mtssile Range. N. Me.s~co. Takeuchi K. (1962) On the non-dimensional rate of dissipation of turbulent energy in the surface boundary layer. .I. .\fL,r. Sot. Jnp. Ser. II 40. 117-125. Taylor R. J. (1962) Small scale advection and the neutral profile. J. Fhid .Ild~ 13. 529-539. Tourin ,M. H. and Hoidale M. M. (1963) Low Iebel turbulence characteristics at White Sands hlissile Range. Tech. Rep. 131. U.S. Army Signal Miss. Supply Agency. U’hitc Sands Missile Range. N. Mexico. Tounsend ,A. A. (1962) Natural convection in the Earths boundary layer Q. J. R. mer. Sot. 88. 51-56. U.S.4.F. (1962) Procrrtiirrys of’ (1 ,Vrrtiorml S,wrposirr~ir o/r CC~irr~is for .Aero.spr~ce CL/tic/e Drsi<gv. U.S.A.F. Gcophy. Res. Div. A.F. Surveys in Geophys. No. I-10. Wilson R. (1961) A note on severe turbulence at Renfreu between 5O@lOOO ft. on 26th Jan. 1961. .LIc,r. .1/q. 91. 131-13-1. Zubkdiskii S. L. (1962) Frequent\ spectra pulsations of the horizontal components of wind wloctty in th< surface layer. Ixt~sri~z .-I. S. L~.S.S.R. Ceoph~:.

mzasuremcnts on an aircraft and at fixed points. R.,A.E.. T.S. Structures 325. Byzova .U. L. (Editor) (1963r Inwsttgatton of the bottom 300 m laysr of the atmosphere. Acad. SKI.. L.S.S.R. [Translated by Israel Pros. for Sa. Trans.. Jerusalem

Cermak J. E I lY65) applied to dtffusion Lagrangian in turbulent similartt) hypothesis shear flow. J. fluid

!LlL’CII.15. 49-h-l.
Davcnoort A. G. (196.1) The r:lattonship

oi wtnd





L. .II.




stresses on water

surfaces: a \\ind tunnrl study. .&a. J. P/ILL 16. -17C-189. Gibson C. H. and Schu-arz IV. H. (1963) The uniwrsal equilibrium spzctra of turbulent kclocities and scalar fields. J. Fluid .Urch. 16. .X-N. Goddard W. B. (1963) Introductory measurements of shear stress across rye-grass sod. Final RLI~ D-\-36-039-X803.X pp. 119-157. Inoue E. (196.:) On the turbulent structure of airtlow within crop canopies. J. .\lct. k. Jq,. II. 3 I7~?25. Jensen Xl. and Franck S. ( 1963) .!loci‘,i TI\r\ 1117idwlr~~r Ili~rct-/. Pir~~ito111~1~7 Lkpdwr oit r/k II iutl Sped. Danish Tech. Press. Copenhagen. Lappe C’. 0. and Davidson 8. (196.:) On the range of Lalidity ofTaylor’s hypothesis and and ths Kolmogorotf spectral law. J. .-lrr~to.s. SC;. 20. 56Y-576. Lappc‘ c’. 0.. Thuillier R. H. and Rec\es R. M. (196.3) D~vslopment ofa IOU altitude turbulence model for estimattng gust loads on aircraft. Tech. Dot. ASD-TDR-6331% Wright Pat. -\.F. Bass. Ohio. Lemon E. R. (196.:) Theoretical constderatton of acrodynnmtc exchange in a turbulent boundar) lay. L.S. 4pric. Res. Sev. Prod. Res. Rep. 71 Lemon E. R. (1963) The energy budset at the Earths surface-11. Prod. Rrs. Rep. 2. .Agrtc. Res. Service.. U.S. Dept. of Agriculture. Lettau H. (1963) Studies oi the cllects of variations in boundary condittons in the atmosphere. I’nic. N’isconsin. .Ann. Rep. 6.3. .AD. 429. 496(2). Markse E. H. (1963) On the relationships of range to standard deviation of ivind tluctuations. .\lwrrir/~~ Il>urlw RH. 91. 83-87. Munn R. E. (1963) .A re-appraisal of Suttons parameter 1,. J. trppl. ,\lrr. 2. -+-LO. Munn R. E. and Richards T. L. 1196;) The micromrtsorolog of Douglas Point Ont. Rep. TEC-455. Xl&. Branch. Toronto. Panofskh H. .A. and Pasquill F. (1963~ The constant of the Kolmogoroff Law. Q. J. R. mc~. Sot. 89. 55&551. Panofsk) H. .A. (1963) Determmation of stress from wind and trmprrature mcasursments Q. J. R. wr. Sot. 89. Sj-94 Poolrr F. i 196.3) i\irtlou o\er a tit) in terrain of moderate relief. J. c~/T/J/. .UtJr. 35. U&-t56. Semenova L. G. and Solomatina I. I. (1963) Some results of microclimatic survebs undzr ruezrd relief conditions, Translated b) Tech.. Scr\ices. -\t.ashin,oton. Soviet investiz. of atmos. pollution. J.P.R.S.: 27. 279 Nov. ‘6-t. OTS:6-I-65l535.

SW.. 1.425.

Brocks K. and Hasse L. (1963) Fluctuation measurements made at sea with a gyroscopic stabilisrd Hoating mast. Abst. m Proc. ljrlr Grh. .Assrr~rh/~. I.L:.G.G.-I.,\.~I.A.P. Bark. Calif. p. I I?. Brook F. A. (1963) Investigation of rnrrgq and mass transfers near the ground including the intluence oi the soil-plant-atmosphere system. Final Rep. Task. 3.A99-27005-08. L’niv. of Calif., Davis. California. Cont. D.A-76039-w.-80331. Buell D.. hfcCullough G. B. and Steinmetz t\‘. J. (1963)

Takeuchi K. (1963) Some studies on the tluctuations of irind direction near the ground. J. IW~. Ser. Jap. 41. -10. Taylor R. J. (196.:) .An analysis of some wind profiles in the atmospheric uind friction la!?r. Met. Proj. 7655. .A.F.C.R.C.. Hanscom Field. Mass.

Idlabatlc Angcll J K;.

atmo spheric and J R.




I 196-l)

\leasurcments of turbulence

of at

Lagrunglan ‘500 ft. Q



,,lr’l. sot. 90. 57-,I. -\pplcb\ J. F. and Ohmstcde

I\‘. D. (196-1) Sumertcal

soluDavenport -\. G. I 19651 II’3.H.J. Iibrld Tml~, Cmrw-iI id Pmyw~r~ R~,pl,r. (Unpubl~shcd) \\.orthlngton. Skelling.

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Helle R: Jackson. New York. Dexon E. L. (1965) Wind gust spdj: aLerapIng time relationship. -III<?. .W<,r. !&lay. 51. 11~ I-! Failer -\. J. (1965) Large eddIes In the atmospheric boundary laker and their posslblr role m the iormaflon of cloud rows. J. 4r1rro.x SC;. 22. 176114. Gurvich .A. 5 (1965) Vertical temperature and \\md \elocit\ profiles in the atmospheric sui-face laber. /:I .trmo.s. Octvm Ph~s. I. 3l-.:6 (Eng. Edn.). Ivanov V. N. (1965) Certain characteristics of the structure of the atmospheric boundark layer. T,.~rt/\. .4kirti. .\‘~:i,.

S.S.S.R. Imr. P~~iklndmi


2. 121..

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1. -lw1os.

Roll H. W. (1965) Physics qt’ t/w Mn~%rc .4rrno.sy/~rrt~. \cadsmic Press. Sew York. S&sac J. (1965) Distribution of the energy of atmospheric


J. Cot hIHA\ Bani, oi -\mcrxa. Stud>. Txh. St. Ln11 H. llorld H Q Bu~lci;::~ P‘lrt II. \V~nd

Shekter F. N. (1965) Solution atmosphsnc boundar) la>?r brat exhsnze into account.

of the structure Trudv

problem of the taking radiatl!c Guofi:. Ohs. 167.

Tunxl orado

Ret: C-ERhh-6:RD\I-JEC and Tlisng L. R 119661


UorduSorlch measurement atmospheric 1--m’\‘&


Shiotani Il. -\ral H. and Hakashida C. (136iJ Vertical distribution of i+lnd \elocitles and Iertical structures of gusts in strong winds. Rallwah Tech. Res. Inst. Jap. Nat. Rl>s. Rep 514. Suanson R. N. and Cramer H. E. (1965) .A stud> of lateral ,md longitudinal intensities of turbulence. J. ~~ppl. .\ltjr. 1. -1OY--I I 7. Tavlor J. ( 1965) .!f‘rrr~ru/ of a.‘c hrt/\. N ;\.T.O.. .A.G.,A.R.D. s3. Pergamon Press. Okford. Townssnd A. -\. (1965) The response of a turbulmt boundary la)cr to abrupt changes in surface conditions. J. FlUill .\/‘,‘,/I. 22. 799. T>ldsle! J. B and \\‘allington C. (1965) The effect of wind shear and \crtical diffusion on horizontal dispersion. 0. J. R. i~lt’r. Sot. 91. 158-I 7-t. I S. l.ihrar> of Congress (1965) Sorirr .\li~~o,,ri,r~oro/o~/~. -\ compilation of abstracts. .Aerospace Tech. Div. ATD Rep. pp. 65-i S. Zbrozck J. K. (1965) .Atmospheric gusts: present state of the art and iurthcr research. J. R. .4muo~cr. Sot. 69. 51; _. Zimmermann S. P. (1965) Turbulent atmospheric parameters h) contamrnant deposltion. J. .4/~/11..\f,,r. 4. 279 sx. Barry P. J. (1966) The wind profile X.E.C.L. 25-4. A.E.C. Ltd.. Chalk Riier. Ontario. Calder K. L. (1966) Concernlnp the slmilarit! theory of Monin and ObukhoR ior the turbulent structure-of the thermally stratiticd surface la)sr of the atmosphere. Q. J. R. wr. Socc 92. Cramer H. E.. Record F. .A. and Tillman J. E. (19661 Round hlll turbulence measurcmcnts. M.I.T. Camb. Dep. of Met Cont. D.~--\.MC-3Y-OJ.:-6j-GIO. Davenport .A. G. (1966) An approach to aind tunnel modclling of the response of structures to the nautral v. ind. Proc. Mrrriuy 011 Growrti CYid Load Prohlrms in Rehiou to Law~ch Vel~icks. NASA. Langley Res. Centre. 7-Y June. Davenport ,A. C. (1966) The treatment of uind loading on tall buildings. Proc. Swp. ot7 ToI/ Builti~~~gs. pp. 44l456 Pergamon Press. Oxford. Deland R. J. and Binkowski F. S. (1966) Comparison of wind at 500 ft over Minneapolis and Louisville with the geostrophic wind. J. Air Pohr. Corlrrol Ass. 16. 107-41 I. Elderkin G. E. (1966) Experimental investigation of the turbulence structure in the lower atmosphers. BattelleNorthwest. Rep. 329. Pacific N.W. Lab. Richland. Washington. Findlater J.. Harrower T. N. S.. Howkins G. A. and Wright H. L. (1966) Surface and 900 mb. relationships. Sci. Paper. Met. Off. Xo. 23 H.ILl.S.0.. London. Gurvich A. S. and Meleshkm B. N. (1966) The determination of the micro-scale of turbulence from Ilght intensity Huctuations. I:r. .4rms. and Ocra17. Phxs. 1. 68%694. Haugen D. .A. i 1966) Some Lagrangian propcrtiss of turbulence deduced from atmospheric experiments. J. appl. .\[a. 5. 616-652. Koloseus H. J. and Davldson J. (1966) Free surface instability correlations and roughness-concentration effects on tlow over hbdrod! namicall) rough surfacts. C.S.G.S. Water SuppI> paper l592-C.D. Kraus E. B. (1966) .Acrod>namic roughness of the sea surface. J. 4rmo.s. SCI. 23. 1. Lcttau H. (1966) Longitudinal versus lateral tdd) length scales. J. .4rmos. Sot. 23. 151-158. .LlcCrsad) P. B. (1966) Mean wind-speed measurements in turbulence. J. oppl. .\fer. 5. 119-X5. Xlarshall R. D. and Cermak J. E. (1966) Wind studies of

oi turbulent ground laher.

%NI~ .tt t\\o hetghts in the 1::. -Irilk~\ Ol~~~iiii P/I!, 2.

Payne F. R and Lumls) J. L. I i366) I-D Srectra d?rl\cd from an airborne H.N’..A 0. J R I;‘~: SIC 92. :I)?. Pond S.. Smith S. D.. Hambl:n P. F. .!nd Burllng R. I\’ (1966) Spectra 0i b?locit> and temperature tluctuations in the atmospheric boun&r) Ia)cr ?\:r the sc,l. J. .-Irmos. So. 23. i-&3X6. Pooler F. J. (I9661 Tracer d:sperjlon o\ir .I clt>. J 4r1, Polltir. Coruroi .4x 16. 677-6s i. Pritchard F. E. (19661 -\ statiirlcd model oi atmospheric turbulence and a review oi the assum:tlons necsssar) for its use, A.G..-\.R.D. Meetiny on Stabllit> and Control. Cambridge l_ nil.. Cambridz. L .K. Pritchard F. E. (1966) The turi!llencc and terrain cn~ironments atlectinn loo altitude High Sneed Flleht. Cornell Asro Lab. Ref: FD4I 39.:. _ Tkachcnko A. \’ (1966) Cocr?icxnt of tt!rhulencc in the atmospheric boundar) Iabe:. I .S..-\.F. S.C Transl FTDMT-6-1-396 pp. Y.:- I UJ. Tourin H. M. and Shrn I\‘. C. (I9661 Deciduous forest dirfilsion stud!. Fmal Rep. \ ol. I DIP. 19 J decid. forest. Appl. Sci. Di\.. Litton Systems Inc. Sl:rneapolls. &Lin. Vaughan I\‘. W. ( 1966) Consldcratlons ani! Phllosophh 01 ground ulnds criteria foundztlon. S..\.S.-\. Asro--\strodynamic Res. Rsb. No. 5 pa. 146 15:. Blackadar A. K. (1967) E\tsrxl paramct::-1 of the mean wind How in the barotropx 5oundarjr !l!:r and Isrgescale atmospheric a<rod>namlcs. Stud! Conf. G..\.R.P (I.C.S.L. 1.L.G.G.. %‘.M.O and G.O.SP..\ R.). Stockholm. Blackadar .A. K. and Chaplin .A. S. (196-r \\‘ind protiles. spectra and cross-spectra o\er homoyrn<ous terrain. Tech. Rep. E.C.O.\I.-Ol.XS-i I \D~S-I-III Penn. St. L nib. Charnock H. and Elhson T. H. I 136’) The boundar> 1a)er in relation to large-scale motions of the &tmosphcre and ocean. Study Conf. G..A.R.P.. II.C.S.U I.L.G.G.). Stockholm. Cramer H. E. er d. (1967) Investigation of IOU Ie\el turbulence structure for various surhce roushnexxs and gross meteorological circulations. \I I.T. Cont. D,A 19-09?ARO-66. Davenport .A\. G. (1967) The dspsndenc: of wind loads on meteorolop~cal paramets:s. Paper _‘. COUP: 0,~ Ili~ti Lo&s 011 Brrildmyx -Univ. Toronto Press. Toronto. Davenport A. G. and Is>umo\ S. ( lY67a) The application of the boundary laker wind tunnel to the prediction of uind loading. Paper 7. CO~I]. <JI: Il’i~~tl LIU& 011 Bllil[ii~~y.s. Univ. Toronto Press. Toronto. Davenport .A. G. and Is\umo\ S. C 196Yb1 -\ u md tunnel stud! for the L’.S. Steel Bulldmg. Ens. Sci. Res. Rep. B.L.W.T.-5-67-Univ. M’. Ontario. Davidson B. (1967) .A summar> of the S.\r’. urban air pollution dynamics Rcssarch Programme. J. 4ir Pohr. Courrol 4s.~. 17. I %lIX. Elderkin C. E. (1967) Comparison of the turbulence spectra from Hanford. U’ashington and Liberal. Kansas. L.S..-\.E.C. Met. Info. meeting. Chal; RILer. Ont.. Canada (Cont. -\T(-l_i-I I-ISXII. Estoque M. A. (1967) Appro\lmatlon to boundar! laber \vind profiles. Tt,/i~r.s 19. 56&‘56. Frizrola 1. .A.. Sineer I. .A. and Busch b. E. I iY67) ,A summar! ofrecent turbulence measurements ;It Brookha\en. BrookhaLen. B.S.L. I ISY9. Hanna S. R. (1967~ .A model oi rxtlcal turhui<nt transport in the atmosphere. Order So. 65-l I. 9Yh. Penn. St. Univ. Hass If.. A.. Hoccker IV. H.. Pack D. H. and -\n~cll J. K. (1967) .Analysis of IOU. level constant \alums balloon Qhts ot?r X.1’. City. Q. J. R uwr. SOL.. 93. Q-493.

Jones urbx Kaimal

P. 41. and arcx J. f. and

\+ ~lsoa C. B. (196-l Rss. Rep.
on a

Wind &id.


in an of
0. J.

C.1 R I.x. Haugsn


SC!. 3. ?I.

Zilitmkc\xh S. S. 2nd Laihhtman D. L. II%-i D!namxs of the .ttmosphxx boundsr~ layer. fx irfriu,. O~~~~ztr. P /7!-5.3. I w- I9 1. Zubko!ski S. L. and Kracchcnko ment T. (1967) Dtrcct P/IN mrasurein 3. i!-“‘.

D. .4. (196’)


vertical vetocit\ RUCtu~tlOllS R. ,,rc’t. Sec. 97’. !0_%3 1 :. .

oi some charscterrstics

ofatmospheric turbulence
4rr~o.s. OCNI.

Kl~nc S. J.. Rtz>nolds I\’ C Schraub F. -\. and Runstadlrr P. \\. (19671 The structur: of turbulent boundar:. layers. j. F!ifi‘f ff4. 30. ‘41 m-73. Lsttau H (19671 Ne\\ hyothssis for the relationship betnern <dd\ rind mi’an 5tatrS. P/I&s. FINiris iSrcp$. l967L 57% 5s.:. Lilt\ D. K. and Pnnofsk> Ii. .A. (19671 Summar) of pm& in research on atmospheric turbulence and diFfu&n. TIXUIS. 4r11.&oyl~xs. L.rriorl 48. &N-15?. .&lcldenhall H. I 1967) .A statistical stud\ of the friction wind veering the planetar> boundar) lay. I. .Atmos. Ei. in Paper. 90. 116.Color. St. Univ. hlonin -4. S. and Zilitmksvich S. S. (1967) Planetar> boundar! In!er and large-scale atmospheric dynamics. Stud! ConT. on G..-\.R.P. Stockholm. Moore D. J. (1967) Meteorological measurements on a I Y? m tower. .4rJlrusyllr,ric Ellriro~r~llelfr I. X7-377. Ohukho\ A. iLz. and k’aglom f\. hf. (1967) Progress in atmospheric turbulence in\sstigations. f:r. .4r/1zos. 0crir11 pi:ts. 3. 7%366. Pandfskv H. .A. and Prasad B. (1967) Similarit! theory and ditiusibn. .-lir Ililr. Poiilrt. 9. 4l9-430. Pasquill F. (1967) Vertical components of turbulence at hctghts up to I NO m. .-lrrr~o.sp/tcrrc Eirrirort,urrlr I. 441 450. Paulson C. ‘4. (1967) Profiles of wind speed. temperature and htlmidit~ ober the sea. Sci. Rep.. Nat. Sci. Foundation. G.P.-I-IIS. Uni\. of Washington. Peterson J. and Panofsk\ H. A. (1967) The non-dimensional wind shear over heterogeneous terrain. Sw.Me\ice St. Univ. L’/ryui~lt,~l Rock Bull~.~ric,s hlt,r. Cou/.. pp.

the near watc’r Iaber. lx.

Bra&\ E. F. il’%i 4 micrometeorological stud.4 of \eloctty profiles and surhce drag m the region modified h! a change of surface roughness. Q. J. R. )wr. sot. 94 361.

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Pinus X. A.. ReIter E. R.. Shur Ci. S. and Yinnichenko N. K. (1967) Power spectra of turhuience in the free atmosphere. K$iits 19. X6-2 L 3. Prasad B. and Panofskv H. A. (19671 Properties or variances of the meteordlogical properties at Round Hill. Tech. Rep. U.S. ‘Arm) EC’OM-0035P. Reiter E. R. and Lester P. F. (1967) The dependence ot‘ Ri on the scale length. Atmos. Sci. Paper So. I Il.. Dept. of Atmos. Sci. Colorado St L’niv. Shellard H. C. (1967) Results ol some recent special measurements m the U.K. relevant to wind loading problems. Paper 19. COJ$: 011 iti/rii Loncfs 0,~ BuiMimJs. Univ. Toronto Press. Toronto. Shlotani M. and .Arai H. I 1967) Lateral structure of gusts m high winds. Paper 10. Co$ OII Il’i~d Lotrdj 011 &ii& i,y.5, Cniv. Toronto Press. Toronto. Singer I. A., Busch Xi. E. and Frizzola J. .%. (1967) The micrometeorology of the turbulent Row field in the atmospheric surface boundary lay. Paper 21. for$ ou IC%tl Lo&s 011 Buiitlrmqs, Univ. Toronto Press. Toronto. Smith S. D. (1967) Thrust anemometer measurements of wind velocit> spectra and of Reknolds stresses over a coastal inlet. J. .Lfni-. Rcs. 25. 239-267. Swinbank \V. C. and Dy A. J. (1967) An erperimentat stud) in micrometeorolog). Q. J, R. mr. SOC. 93. 19C 500. Tritton D. J. (1967) Some new correlation measurements in a turbulent boundary layer. J. Fluid .\fd~. 28, 439462. Weiler H. S. and Burlington R. W. (1967) Direct measurements of stress and spectra of turbulence in the boundar! layer over the sea. 1. .&t?ros. Sci. 24. 62:X,64. W.hl.0. i 1967) Global atmospheric Research programme (G..%R.P.). Report of Stud? Conf. VolkoLitskaya Z. I. and Ivanov V. i\;. (1967) The low frequrnc!. boundary ol’ the inertial interval in the atmospheric boundary layer. 1~. -Irms. Ocrm. P/I~. 3. IO I English Edn).

Fichtl G. H. (196ba~ -Xn ansl>sis ol the roughness icngth .associatrd with the X.4.S.A. 150 m. !+I& Tower. XA.S.;\. T.hI.S.-53690. G.C. Marshall Space Flight Centtt. Alabama Ftchtl C. H. (l%Sb~Charactzristics of turbulltncc observed at tht X,.&S..\. 1SOm XIet. Tcmcr. j. Lippi. .Clc~. 7. S?S. Gault J. D. and Guntetr D. E. (1968) Atmospheric turbulencs considerations ior future aircraft designed to opsrarc at low altitudes. .A.l..X.-i. Paper No. 63-216. Graham I. R. (1368) .An analysis of turbulence statistics at Fort Wn~nc. Indiana. J. r~ppl. ,\lrr. 7. 9?-9% Harris R. I. (196s) Msasurtment of wind structure at heights up to 5% it. aboLL2 = Oround level. Conf. on %‘ind Loads on Buildings. Loughborough Gniv. Harris R. 1. (1968) On ths spectrum and atito-correlation function of gustiness in high winds. E.R.4 Tech. Rep. j27?. Haugsn D. ,A. and Kaimal J. C. (1968) Characteristics of vertical fluctuations obxrbed on a 430 m tower. Q. J. R. twr. Sot. 94. 412. Helliwell N. C. (1968) Some open scale measurements of wind over central London. Symp. 011 C.&U Clifxar‘x t\;..5I.O.. Br\lssels. H.M.S 0. i 1965) Tables of surface wind speed and direction o\er the U.K. Net. 0tY1c:. Met, 0,792. James K. \V. and bloore D. J. (1968) Thermal roughness. .Irrnojpllrric EItrirolrtnrrlr 2. 628. Jones P. M. rr c7i.(1965) Some measurements of urban wind velocrt) profiles in the first 1000 ft. SUU~X ou L&III Clittnrrfs. U.iit.0.. Brussels. Lenschow D. H. and Johnson W. B. 11965) Current airplane and balloon measurements or atmospheric boundary la)er structure over a forest. J. czypl. .\l~. 7. 79-85. Lrttau H. (I9681 .:-D turbulence m uni-directional mean fio~. ECOM 66-G11-.A. Tech. Rep. 196667. Grant lie. D4-12vIC-7Y-O4~-66G24 pp. 127-116. Unir. of t\‘isconGil.

McBean G. A. (196Yk inlsstigation rtn ths forest. J. appl. .\lrr. 7. 110416. hlsrons\ R. H. (1965) Characteristics lencein and above model forests.




of umd and turbuJ. trpfi. .\/dr. 7. 7S&


J. COC\IHA\. Kalmul J. C. I lYh91 \lcasurem<nt oi momr’nt:lm and heat tiu\ In the surf~lce houndar) labcr. R&lo &,I. -1. I IIT-


H. .A. (196s)


of current


on wmd

I 1-3.
Kaimal J. C. and Haugcn D. 4.

propertiss rsls\ant for diffusion in the lowest I(X) m. .%mdla Corp. S!.~rry. 0,) 7i&1l<,~rc~, ~~rrtl Diffi,sro/~. Panofsk> H. .A. and Mares E. (1968) Recent measurements of co-spectra for heat tluu and stress. 0. J. R. wr.

I lY6Y)





94. 53 IL%5
Pxrx F. J. and

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itresj diagnostic

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