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The turbulent transfer mechanisms in the atmospheric surface layer McBean, Gordon Almon 1970

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THE TURBULENT TRANSFER MECHANISMS IN THE ATMOSPHERIC SURFACE LAYER by . GORDON ALMON McBEAN B.Sc, University of B r i t i s h Columbia, 1964 M.Sc, McGill University, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics and < Ins t i t u t e of Oceanography We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1970 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f r ee l y ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wri t ten permission. Department of Physics The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT The objective of t h i s study was to investigate the turbulent transfer mechanisms near the surface. Direct measurements of the turbulent fluxes of momentum, heat, and moisture were made i n the atmospheric surface layer: p r i n c i p a l l y , 2 m above a grass surface at Ladner, Canada, and for comparison 8 m above the A t l a n t i c Ocean near Barbados. The spectral c o r r e l a t i o n c o e f f i c i e n t s were considered to be a measure of the transfer e f f i c i e n c y as a function of scale s i z e . For momentum trans-fer the e f f i c i e n c y decreased at a l l scales as i n s t a b i l i t y increased. It was postulated that t h i s was due to greater amounts of momentum being trans-ferred i n bursts of short duration, thus making the spectral c o r r e l a t i o n c o e f f i c i e n t , averaged over s u f f i c i e n t time, smaller. The Ladner r e s u l t s for heat transfer showed that i t s transfer e f f i c i e n c y increased at a l l scales when i n s t a b i l i t y increased. The r a t i o s of the transfer e f f i c i e n c y of heat to that of momentum were greater than 1 for most scales, even for near neutral s t r a t i f i c a t i o n s , and increased to between 2 and 3 for more unstable conditions. The e f f i c i e n c y of moisture transfer, when moisture i s a passive s c a l a r , was usually smaller than that for heat transfer and was found to depend on the c o r r e l a t i o n between moisture fluctuations and those of temperature, which i s the active s c a l a r . The res u l t s from Barbados pointed out two main differences between the subtropics and mid-latitudes: that the temperature spectrum i s much narrower i n bandwidth and that the humidity fluctuations make an equally important contribution to buoyancy. These features are re f l e c t e d i n the transfer mechanisms. i i i TABLE OF CONTENTS page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES i v LIST OF FIGURES v LIST OF APPENDICES v i i i ACKNOWLEDGEMENTS i x 1 INTRODUCTION 1 2 THEORETICAL BACKGROUND 3 3 THE EXPERIMENTS 9 3.1 The Ladner Experiment 9 3.2 The F l i p Experiment 13 3.3 The Equipment - 15 3.4 Summary of Data Presented. 19 4 THE TURBULENT TRANSFERS OF MOMENTUM, HEAT, AND MOISTURE 24 4.1 Time Series Representation 24 4.2 Cospectra of the Transfers of Momentum, heat, and Moisture 28 4.3 Spectral Correlation Coefficients 34 4.4 Correlation Coefficients 47 4.5 Consideration of K^ /K^  52 5 TURBULENT TRANSFERS DURING BOMEX 56 5.1 Special Analysis for F l i p Data 56 5.2 Comparison of the Turbulent Transfers During BOMEX 62 5.3 Turbulent Transfers: BOMEX and Ladner 73 6 SUMMARY 74 BIBLIOGRAPHY 76 APPENDICES 79 iv LIST OF TABLES page I S t a b i l i t y Groups for Ladner Data 22 II Comparison of Correlation Coefficients for Two Pairs of Data 41 I I I Effects of T i l t Angle on Drag Coefficient and w variance 64 IV D i g i t a l Sampling Frequencies 80 V LIST OF FIGURES Figure Page 1 A i r photograph of Ladner experimental s i t e 10 2 Map of Ladner s i t e showing wind directions for each run 10 3 Photograph of measuring instruments for Ladner experiment 12 4 Photograph of F l i p , i n dicating instrument loc a t i o n 14 5 Schematic of instrument-recording system for Ladner experiment 16 6 Summary of data: wind speed against s t a b i l i t y 21 7 Time series traces of w'q', w'T', and u'w' 25 8 Composite momentum transfer cospectrum for Gp. I 29 9 Variation of momentum transfer cospectrum with s t a b i l i t y 29 10 Composite heat transfer cospectrum for Gp. I 31 11 Variation of heat transfer cospectrum with s t a b i l i t y 31 12 Coherence and phase angles for stable conditions 33 13 Composite moisture transfer cospectrum for Gp. I 35 14 Variation of moisture transfer cospectrum with s t a b i l i t y 35 15 Spectral c o r r e l a t i o n c o e f f i c i e n t s for momentum transfer for Gp. I 36 16 Variation of momentum transfer spectral c o r r e l a t i o n c o e f f i c i e n t s with s t a b i l i t y - 36 17 Spectral c o r r e l a t i o n c o e f f i c i e n t s for heat transfer for Gp. I 39 18 Variation of heat transfer spectral c o r r e l a t i o n c o e f f i c i e n t s with s t a b i l i t y 39 19 Spectral c o r r e l a t i o n c o e f f i c i e n t s for moisture transfer for Gp. I 40 20 Variation of moisture transfer spectral c o r r e l a t i o n c o e f f i c i e n t s with s t a b i l i t y 40 Spectral correlation coefficients for runs L221/2 and L222/2 Spectral correlation coefficients for runs L224/4 and L311/2/1 Spectral correlation coefficients for moisture transfer averaged over s t a b i l i t y Groups I to VI The ratios of the spectral correlation coefficients for heat transfer to those of momentum transfer Variation of the correlation coefficients for momentum, heat, and moisture transfer with s t a b i l i t y Variation of the ratio of the correlation coefficients o heat transfer to those of momentum transfer with s t a b i l i t y Variation of the ratio of the correlation coefficients o moisture transfer to those of momentum transfer with s t a b i l i t y r j " / z ^ against s t a b i l i t y Variation of K^/Kj^ with s t a b i l i t y Effect of Flip's response to ocean waves on w-spectrum and uw-cospectrum Effect of t i l t on uw-cospectrum; run B14/2 Cospectra of momentum, heat, and moisture transfer for Flip experiment Spectra of temperature and humidity fluctuations for Flip experiment Temperature-humidity spectra correlation coefficients for Flip experiment Spectral correlation coefficients for run B14/1 Spectral correlation coefficients for run B15/3 IOUBC spectral analysis system The low frequency analysis transfer function and i t s effect on spectra Comparison of three spectral analysis techniques Check on low frequency a n a l y s i s by comparing overlap o f a n a l y s i s region Comparison of spectra o f Lyman-rx humidiometer and dew point hygrometer v i i i LIST OF APPENDICES page I Spectral Analysis 79 II Humidity Analysis 89 III Tabulation of Results: Ladner 94 IV Tabulation of Results: BOMEX 101 V Spectral Analysis Results 103 i x ACKNOWLEDGEMENTS I am deeply grateful for the assistance of many people i n the r e a l i z a t i o n of t h i s study. I would l i k e to thank Dr. M. Miyake, my thesis advisor, Dr. R.W. Stewart, and Dr. R.W. Burling for t h e i r h e l p f u l advice at a l l stages of th i s study. The main experiment was conducted at Canadian Forces Station Ladner and I am grateful to Capt. D.W. Bastock, the base commander, and his personnel for t h e i r complete cooperation. During the Barbados experiment the temperature and humidity measurements were made with equipment of Dr. S. Pond of Oregon State University. I am especially g r a t e f u l to Dr. Pond for his careful operation of the equipment and for making the data available to me. A l l the students and s t a f f at the Ins t i t u t e of Oceanography, University of B r i t i s h Columbia (IOUBC) helped at various stages of t h i s study and I am grateful for t h e i r assistance. M.A. Donelan and J.A. E l l i o t t deserve s p e c i a l thanks. I would l i k e to thank the Canadian Meteorological Service for supporting me while on educational leave. Last I would l i k e to thank most of a l l my wife P a t r i c i a for her encourage-ment and help throughout my study. " -1 CHAPTER I INTRODUCTION The turbulent transfer processes play an important role i n determining the motions of the atmosphere and the ocean. The atmosphere functions as a heat engine by receiving heat input from the surface i n the forms of la t e n t and sensible heat due to turbulent transfer and i n the form of long wave radiation. The winds drive most of the ocean surface currents by transfe r r i n g by turbulence momentum both into the waves and d i r e c t l y into the current. Further knowledge of the turbulent transfers of momentum, heat and moisture are thus e s s e n t i a l to a further understanding of the whole c i r c u l a t i o n s of the atmosphere and ocean. The aim of t h i s thesis i s to investigate the trans-f e r mechanisms of the v e r t i c a l transport of momentum, sensible heat, and moisture near the surface and to discover t h e i r s i m i l a r i t i e s and d i s s i m i l a r -i t i e s . To study the transfer mechanisms i t i s e s s e n t i a l that d i r e c t measurements of the fluxes be made. Further, the re s u l t s of d i r e c t measurements should be examined both i n the time domain and i n the frequency domain. I t i s by anal-y s i s i n the frequency domain that, through Taylor's hypothesis, the effects of di f f e r e n t scales of atmospheric motions can be investigated. Because the three transfers of momentum, heat and moisture are a l l very important i t i s necessary to study them simultaneously i n order that possible interaction can be examined and so that t h e i r transfer mechanisms can be compared. In the past considerable e f f o r t has gone into studying these transfers. However, usually one or more of the above measurements was missing. Studies have been made of the p r o f i l e s alone i n attempts to understand the transfers by measuring an ef f e c t of the transfer rather than by d i r e c t measurements. 2 Recently more di r e c t measurements have been made (e.g. Dyer, 1965, 1968; Mordukhovich and Tsvang, 1966) but the frequency domain was not investigated. Businger et a l (1967) studied heat transfers and Smith (1967), Elderkin (1968), Weiler and Burling (1967) and Miyake et a l (1970) studied momentum transfers i n the frequency domain while Zubkovsky and Koprov (1969) studied both. This thesis represents the f i r s t simultaneous d i r e c t measurements of a l l three transfers f o r which the results have been analysed extensively i n the f r e -quency domain. 3 CHAPTER 2 THEORETICAL BACKGROUND The equations of conservation of momentum and mass and the entropy bal-ance are fundamental to a l l problems of geophysical f l u i d dynamics. For atmospheric flows near the earth's surface an additional equation, that of conservation of water vapour, is frequently required. For turbulent fluids i t is normal to use a Reynolds-type separation of mean and turbulent parts. This plus assumptions based on ai r behaving lik e an Ideal gas, lead to (see Lumley and Panofsky, 1964, p.59; P h i l l i p s , 1966, p.7): The terms in these equations due to the turbulence are the Reynold stresses, p u ^ ' u ' t h e turbulent transport of sensible heat (or enthalpy), p C p u^'T', and the turbulent advection of moisture, p u^'q', where q is the specific humidity. A l l other terms are standard notation; a l i s t of symbols is given at the end of the thesis. Near the surface and over terrain homogeneous for scales large relative to the height i t is usually possible to neglect the molecular terms and to assume horizontal homogeneity. This leads to three 4 predictor equations for the local horizontal momentum, pu-^, the heat content per unit volume, p cp T and the moisture content per unit volume,p q: ^_ p u , ^ _ V P - p J l s u z - \ - p u . ' u l l-r-l (2.2) 3 Note that the effects of the radiation flux divergence have been assumed negligible in obtaining (2.2b). A typical value of q is about 10 g/Kg for the Ladner experiment and about 18 g/Kg during BOMEX. To use these equations i t is necessary to specify the turbulent fluxes p U,'u' 5 ^ p c p U^T'and p Cj^ . These fluxes are hence essential to further the understand-ing of the dynamics of the lower atmosphere. For steady-state conditions within the constant flux layer U/Vj' = W 'w' . iA^'T' - w'T'and U$ %' ~ ^ fa a r e constant with height. In order to examine these fluxes more completely they can be represented in a spectral form as: U LAX' / n II where, for example, 0,„,(n) dn is the contribution to the u-w covariance due uw to those eddies with frequencies in the range n to n + dn. I t would be desir-able that the limits of integration, which may be different for each integral, include a l l frequencies that contribute to the flux, yet, at the same time, exclude those frequencies associated with large time scale trends. I t i s only by f i r s t computing and then examining the cospectrum that the limits of inte-gration can be determined. The cospectra can be normalized so that, for example: 1 din n - 1. (;•*) 2 Thus n 0 u w(n)/u^ or n0^(n)/w~*TT are measures of the relative importance of scales associated with frequency n to the tot a l transfer. Taylor's hypoth-esis is that A=u/n, where % is the wave length. In this thesis the "non-dimensional frequency", f, defined as f = z/^K - nz/u, where z is the lev e l of observation, w i l l normally be used. Of special importance to examining the transfer mechanisms are the spectral correlation coefficients: These are measures of the transfer efficiency associated with any particular 6 scale. Note that the spectral correlation coefficient provides different information than the cospectrum. For example 0 u w ( f ) / u ^ and 0 ^ ( f ) / w f T T may have different shapes yet, R u w ( f ) and Rwrp(f) can be similar. Thus the cospec-trum specifies which scales are important to the total transfer but the spectral correlation coefficient is an actual measure of the transfer e f f i c -iency as a function of scale size and hence is more directly related to the transfer mechanism. The importance of the spectral correlation coefficient appears to have been neglected in the literature. Zubkovsky and Koprov (1969) presented data on R u w ( f ) and R^r^f) but placed more emphasis on the cospectra. Weiler and Burling (1967) and Smith (1967) also analysed R u w ( f ) . The behaviour of R (f) and the dependence of R (f) and R .-(f) on wqv ' r uwv ' wTv J s t a b i l i t y has not previously been investigated. In this thesis the three transfers w i l l be examined for s t a b i l i t y dependence based on the non-dimensional s t a b i l i t y parameter, z/L (Monin and Obukhov, 1954). This is defined here as: z/L 4 G t , T ^ ) ] _ * 1 1 <37> - ^ l f o.u J 7 ' (zio) - 2 / L T • ZA*,. is what is usually defined as the Monin-Obukhov length. The correction due to moisture content, L^, can be important over water but is usually negligible over land surfaces. The c r i t e r i a for the similarity of the transfer mechanisms i s , for a given z/L, that the spectral correlation coefficients agree scale by scale for a l l scales associated with the transfer. In other words, the transfer mechan-isms for momentum transfer and for heat transfer can be considered similar only i f R u w ( f ) = R^Cf) for a l l f. It i s useful to be able to compare the overall transfer mechanisms regardless of scale. The correlation coefficients can be defined, as usual: ur'T* The ratios p _/ f or T / C are measures of the relative efficiencies of wi uw wq uw the transfer mechanism for heat or moisture transfer compared to that for momentum transfer. In the literature i t is more common to investigate the similarity by comparing the exchange coefficients or turbulent d i f f u s i v i t i e s : r W T T (7.1) K M The ratios and K^/K^, which are usually considered, are more measures of the transfer effects than measures of the transfer mechanisms. For example, i s a measure of the type- of profile ^ , that w i l l result for a given value of the momentum transfer. The ratios and K£/K^ are, however, closely related to V yn/f1 , and V /V since: W X U.W 1 1 X ' 1 PooT wq uw KM r r /te 2t l i1 n (29.1) Experimental evidence (Tsvang, 1960; Garratt, 1969) indicates that the term in the square bracket in (2.9a) is near unity for unstable stratifications. This implies that (J\ /5j — ^/<^T or that the relative variances of u to T are uniquely related to the local gradients. In the past the ratios KJJ/K^ and K^/K^ have been investigated either by directly measuring both the fluxes and the gradients, as was done by Dyer (1965, 1967) and Mordukhovich and Tsvang (1966) or by investigating the pro-f i l e s alone, since: _ K KM " V aj/ji >l (e.g., Swinbank and Dyer, 1967). In summary i t should be pointed out again that the spectral correlation coefficient i s the most fundamental measure of the transfer mechanisms. Fur-ther, similarity of the transfer mechanism of two transfers can only be shown by showing that the spectral correlation coefficients of each transfer are similar for a l l scales. 9 CHAPTER 3 THE EXPERIMENTS The data used in this thesis are from two separate experiments. The main source of data was from an over ground experiment at Ladner, British Columbia. The other source of data was an experiment conducted by an Institute of Ocean-ography group on F l i p , the floating instrument platform of Scripps Institution of Oceanography, University of California, San Diego, as described by Rudnick, 1964, during the Barbados Oceanographic and Meteorological Experiment (BOMEX) near Barbados. These two experiments w i l l be described in the next two sections of this chapter. The equipment, much of which was common to both experiments, w i l l be described in Section 3.3. 3.1 The Ladner Experiment. The Ladner experiment was conducted over an unused airport at Canadian Forces Station Ladner in mid-August, 1969. This station is at 123.03° west and 49.05° north and located in the f l a t delta region of the Fraser River. The terrain around the station (Fig. 1) i s f a i r l y iniform in elevation and vegetation. A l l data were collected in winds ranging in direction between 160° and 330° "true' (see Fig. 2 for the mean wind direction for each run). For winds from 142° through to 192° the fetch was over about 30 km of water (Strait of Georgia and Boundary Bay), then over a dyke r i s i n g 2 m above land level followed by 1 to 1^ km of mown grass surface (interrupted by one runway) to the observation point. The runways were asphalt and 40 to 60 m wide. For winds from 192° to about 230° the over-water fetch was interrupted by a h i l l y peninsula 5 to 10 km from the observation point. For winds between 230° and 330° the fetch was over several kilometers of mixed farmland and then over about 800 m of grass (again except for one or two runways) before Figure 1. A i r photograph of Ladner experimental s i t e . Figure 2. Map of Ladner s i t e showing wind di r e c t i o n s for each run. 11 the observation point. The portable instrument mast was always located near the upwind edge of a runway during each run. The 10 cm diameter aluminium instrument mast was 4.3 m high, and sup-ported by a tripod clamped at the 0.75 m level. The mast i t s e l f could be rotated about i t s v e r t i c a l axis to orientate a l l the instruments into the mean wind direction. Cup anemometers were mounted 30 cm to one side of the mast at the 1 m, 2m, and 4 m levels. A l l turbulence sensors were mounted on a 3 cm diameter pipe extending 85 cm horizontally from the mast (see Fig. 3). This was mounted so that the centre of a sonic anemometer array was at the end of the pipe and 2 m above the surface. A dew point hygrometer probe and a i r intake for the humidiometer were a l l mounted within the sonic array. A hot wire anemometer, fast response platinum resistance thermometer and thermistor bead temperature sensor were mounted on a ve r t i c a l support arm 40 cm to the side of the sonic anemometer. A Lyman-oc humidiometer and sonic anemometer preamplifier box were also mounted on this horizontal pipe. Most electronics and the recording equipment were housed in a 4'x6Tx6t instrument t r a i l e r located 50 m to the east of the mast. The Ladner experiment began on August 15, 1969. Three data runs were made during the evening of August 15th and another seven runs were made on August 16th (see Appendix III for a summary of the data runs). During these runs the humidity sensors and fast response anemometer and thermometer were not used. When the experiment continued on August 21 the humidity and fast response sensors were used. Twelve data runs were collected on August 21st; thirty-three on August 22nd; twenty-five on August 23rd and twelve on Aug-ust 24th. The program was concluded in the early afternoon on August 24th due to rain. A summary of the prevailing weather conditions for each day is as follows. The weather on August 15 was mainly cloudy while on August 16th i t was mainly sunny. On both days the winds were southerly. August 21st; scattered cumulus and heavy cumulus with southerly winds changing to westerly by the end of the day. August 22nd: clear with winds from the northwest but shifting to southwest by midnight. August 23rd: sunny with scattered alto-cumulus castellanus in the afternoon. Winds were generally westerly becoming light southerly in the evening. August 24th: scattered to broken altocumulus becoming thicker as the day progressed. A few showers in the afternoon and evening. Winds southerly. 3.2 The F l i p Experiment F l i p (see Fig. 4) is a manned spar buoy designed to provide a stable platform at sea. I t can be towed with i t s long axis horizontal to the experimental s i t e . Once on position ballast tanks are flooded such that F l i p adopts a stable position with i t s long axis v e r t i c a l . Of the total length of 116 m only 26 m are above water and i t s effective center of mass is 60 m below mean water line (Rudnick 1967). Because of Flip ' s shape, her v e r t i c a l motions correspond to wave motions about 60 m below the surface which are much less than those of surface waves. D uring periods of this experiment the main F l i p motions were t i l t i n g about horizontal axes due to waves and a rotation about i t s v e r t i c a l axis due to di f f e r e n t i a l wind forces. These and their effects on the data w i l l be discussed further in Chapter 5. - . BOMEX was a large multi-institutional experiment involving a dozen oceanographic ships and more than two dozen aircraft. The objectives and operational setup of BOMEX have been described by Kuettner and Holland (1969). The F l i p experiment was only a small part of BOMEX but i t s t i l l involved two teams of ten scientists each for two week periods. IOUBC cooperated with Oregon State University (OSU), University of Washington, 15 and University of California, San Diego. A three dimensional sonic anemometer-thermometer and the Oregon State University Lyman-<X humidiometer (Phelps et a l , 1970) were mounted approximately 8 m above the mean water surface and 16 m to the starboard side of Flip's h u l l (see Fig. 4). The sonic anemometer was mounted upside-down below a 5 cm diameter horizontal pipe. The Lyman-tf humidiometer was mounted 15 cm further outboard and at a sli g h t l y higher level. These instruments were about one metre directly below and upwind of the horizontal open l a t t i c e support beam which was one half metre wide. A platinum resistance wire thermometer (see Phelps et a l , 1970) was mounted so that the platinum element was approximately 5 cm in front of and sli g h t l y below the intake port of the Lyman- ex. . A resistance wire wave gauge was supported from Fli p ' s lower deck. The data reported here were collected on May 6, 1969, and coincided with ai r c r a f t measurements by the Institute of Oceanography .The remaining data w i l l be analysed later. 3.3 The E quipment The principle of operation, advantages and limitations of the equipment used w i l l now be described. Since most of the equipment is commercially available the descriptions w i l l be brief and references given to the appropri-ate instruction manuals or published reviews. A schematic diagram of the instrument setup for the Ladner experiment is given in Fig. 5. A l l e l e c t r i c a l signals were recorded on a 14 channel instrumentation tape recorder (Ampex Corp., Model FR1300). The tape recorder was operated in the FM mode so that at l\ ips (the tape speed used at Ladner) frequencies from DC to 2.5 Khz could be recorded. During the F l i p experiments a tape speed of 1 7/8 ips was used so that the response was limited to 625 Hz. A l l input signals were kept within the range of t. 1.5 volts while the tape 16 output m o n i t o r t a p e r e c o r d e r input m o n i t o r u 6 a> +-> co CO bo C • H t 3 U O a a> • I - H - H C C a> CU e • H CD st % c 0) • H U CD CL) , C c 4 J X) CO 4-1 o 5H o O • H q-i +-> CO S CD .fi CJ C O L O a; 3 W) • H 17 recorder noise level was about 20 mv peak to peak. A meter panel was con-structed so that the input or output signals of each channel could be mon-itored. During data runs the outputs from the reproduce heads of the tape recorder were always monitored so that the quality of recorded signals at DC and low frequency (less than 1 Hz) could be visually checked. A six channel chart recorder (Clevite Brush Model 260) was used to follow more rapid fluctu-ations (to 100 Hz). The principal measuring device used in the measurement program was a three dimensional ultrasonic anemometer-thermometer (Kaijo Denki, Model PAT-311-l). This anemometer has been described by Mitsuta (1966) and i n -corporates the advantages of both the pulse and continuous wave type sonic anemometers. Three 20 cm long sound paths are used to determine the three wind components. One path is mounted ve r t i c a l l y and the other two are in a horizontal plane and separated by 120°, to avoid structural interference. The effect of the path length is to l i m i t the wavenumber resolution of the sonic anemometer to scale sizes of about 1 m. The noise level of the tape recorder was equivalent to 11 4 cm sec-1 on the sensitivity usually used ( f u l l scale t. 3 m sec--'-). The maximum error in calibration was "t 2%. Sound v i r t u a l temperature fluctuations are measured by sensing the fluctuations in the mean speed of sound along the v e r t i c a l path length. The sound v i r t u a l temperature fluctuations, Ts'v, are related to the temper-ature by (Kaimal and Businger, 1963): where c is the speed of sound and e is the vapour pressure. The maximum error in equating T' and T g v T w i l l , for the Ladner experiment, always be less than 20%; about 12% due to velocity contamination and 8% due to 18 humidity contamination. During BOMEX the humidity contamination errors were much larger so that the sonic temperature was not used. Atmospheric humidity is one of the most d i f f i c u l t parameters to measure. The physical principles and a variety of methods are described in a four volume series under the general editorship of A. Wexler (1965). The two sensors used in this study are commercially made versions of .sensors reported on in the series. The Lyman-cx humidiometer (Electromagnetic Research Corp-oration, Model B) is described by Randall et a l (1965). I t senses the water vapour content of the a i r by measuring the absorption of Lyman- 0c" radiation (1215.6A) across about a 1 cm path length. In this study the response and sensitivity of the sensor were limited by a 65 cm long tube (3.5 cm diameter) used to transport the ai r from an intake within the sonic array to the humidi-ometer. The tube was considered necessary as the humidiometer electronics were too large to put near the sonic anemometer. The effects of this tube and the corrections made for i t w i l l be discussed in Appendix II. To add to the confidence in the humidity measurements, a second humidity sensor, a dew point hygrometer (Cambridge Systems, Model 137-C3), was used in conjunction with the humidiometer„ This instrument measures the dew point temperature by sensing photoelectrically the formation of dew on a mirrored surface and then measuring the temperature of the surface (Francisco and Beaubian, 1965). The platinum resistance thermometer used in this system is relatively easy to calibrate and i t s calibration is quite stable. The dew point hygrometer was thus used to provide an " i n s i t u " calibration for the faster responding Lyman-0( humidiometer. The following relation, derived in Appendix II, was used to relate humidity and dew point temperature fluctu-ations. / % 19 The humidiometer and dew point hygrometer had very similar spectra for fre-quencies below 0.05 Hz (see f i g . 41). In addition to the sonic thermometer, a fast response platinum wire resistance thermometer was also used. This system is constructed by National Electrolab, Vancouver, who modified an I0UBC design (Pond, 1965) and employs an 80 KHz A.G. bridge with less than O.Ol^C overheat. The probes are 0.25 micron diameter platinum wire with a resistance of about 800 ohms. The response at high frequency is f l a t throughout the range of temperature fluctuations. The 0SU resistance wire thermometer used during B0MEX is of similar design but employs 2.5 micron diameter probes of resistance near 60 ohms. The mean wind speeds at three levels (lm, 2m, 4m) were measured with cup anemometers (Makino Photoelectric Anemometers, Model AF 701). The cups were calibrated in the low wind speed wind tunnel of the Department of Mechanical Engineering of U.B.C. A hot wire anemometer (Disa Type 55D05) was used to extend the frequency analysis range for the longitudinal wind fluctuations. During the Ladner experiment both the resistance wire thermometer and hot wire anemometer were calibrated 'in s i t u ' against the sonic anemometer-thermometer by comparing the low frequency spectral densities. 3.4 Summary of Data Presented For the Ladner experiment the data were divided into 91 data runs of 12 to 17 minutes duration. Two longer runs L300L and L307L which were 54 min. and 47 min. respectively included several shorter runs. A complete l i s t of the data runs, their dates, durations, wind speeds and s t a b i l i t i e s are in Appendix III. A l l the Ladner experiment times are in Pacific Day-20 light Saving Time while those for BOMEX (in Appendix IV) are in GMT. For those runs where z/L^ is zero no humidity flux measurements were available. A plot of wind speed against s t a b i l i t y is given in Fig. 6. The different symbols represent different days observations. The results show, as expected, that for higher wind speeds the s t a b i l i t y tends to be near zero. Note further that during most of the stable cases, u<2 m/sec with the lowest speed being 1 m/sec. For these low wind speeds the humidiometer did not ventilate properly and any results from these runs must be treated with extreme caution in con-siderations involving measurements of moisture. In order to analyse the Ladner data systematically the data were divided into s t a b i l i t y groups. These groups and their limits are indicated in Table I. : Groups VI and VIII can each be further subdivided because of differences in results. Gp. VI includes three runs for |z/L|<0.01 which w i l l not be included in plots involving temperature because T* is approximately zero. Gp. VIII appears to change character around z/L =4.0 but a l l runs are low wind speed cases. Group VIIIB w i l l refer to those runs for which z/L> 4.0. To consider the effects of s t a b i l i t y on spectral shape the following procedure was used. For each group a composite plot of seven spectra was plotted and a mean value for each of 10 frequency bands ( ALog^F = 0.5) determined. For groups with more than'seven runs, the plotted runs were chosen by choosing every second run when liste d chronologically. Low wind speed cases and incomplete data runs were excluded when possible. On the averaged cospectra that are presented, the means for Group I w i l l be repre-sented by (.), for Group VI by a (+), and for Group VIIIB by a (v). In addition the standard error of the means w i l l be indicated by the use of horizontal lines; " ~ for Group I, for Group VI, and for Group VIIIB. The original composite cospectrum for Group I w i l l also be presented. 03 a ID' 3CO ni" W + ftft + » ID LciclnGr Aug 15 & 16 A .21 + 22 X 23 5? 24 Z BOMEX May 6 o o a" T - 1 . 0 -0.75 -0.5 -0.25 0.0 0.25 0.5 0.75 Z/L Figure 6 . Summary of data: wind speed against s t a b i l i t y . 1.0 10. Table I. Sta b i l i t y Groups for Ladner Data Group Limits of z/L No. of I -0.63 -0.46 7 II -0.46 -0.34 9 III -0.34 -0.18 19 IV -0.18 -0.10 17 V -0.10 -0.04 23 VI -0.04 0.10 8 VII +0.1 1.0 4 VIII 1.0 : 10.0 6 The original composite cospectra or spectral correlation coefficients for Groups III, V, VI, and VIIIB are given in Appendix V. A complete tabulation of a l l the integrated s t a t i s t i c s is given in Appendices III (Ladner) and IV (BOMEX). The F l i p data analysed were a l l for . May 6, 1969. Five data runs of 45 minutes each were analysed and the results are presented in Chapter 5. A l l F l i p experimental data were for unstable conditions. 24 CHAPTER 4 TURBULENT FLUXES OF MOMENTUM, HEAT AND MOISTURE 4.1 Time Series Representation Time series traces of w'q', w'T', and u'w' representing unstable, near neutral, and stable stratifications are presented in Fig. 7. Note for case L220/1/1 (an unstable case, z/L = -0.47) that the transfers are dominated by periods of active transfer; longer series show that these are typically about a minute duration. Separating these periods are quieter periods of approximately the same duration. During the active periods there is a pre-ferred direction of transport while during the quiet periods the direction is more random. Even within the active periods there are shorter time scale variations between active and quiet periods. Visual inspection of the traces seems to indicate that the momentum transfer has a lower correlation coefficient than either heat or moisture transfer. For the neutral case (Fig. 7b) w'T' i s usually non-zero but there is no preferred direction of transport so when averaged over time, w'T' is near zero. However, there is s t i l l appreciable moisture transfer. The active periods that dominated the unstable case are now not evident. For the stable record (Fig. 7c, z/L = 0.29) the transfers are a l l significantly reduced in magnitude. The scales are only one-quarter of the magnitude of those of Figs. 7a and 7b. The scale and trace (Fig. 7c) for w rT r are inverted. In this case there i s some heat transfer (downwards) but very l i t t l e moisture transfer. Although there are periods of relatively high heat transfer the transfers are generally more continuous in time than they were for the unstable case. 4.000 CHANNEL 7 W'Q' L220/1/1 -4.000. 4.000 LO 30.0 60.0 ^  '90.0 SECONDS CHANNEL 6 W T ' L220/1/1 -4.000J 4.000 SECONDS CHANNEL 5 U ' W L220/1/1 120.0 150.0 150.0 -4.000J 150.0 Figure 7a. Time series traces of w'q', w'T', and u'w' Run 220/1/1, z/L = -0.47. 26 4.000 CHANNEL 7 V PQ • L309/2/2 -4.000J 4.000 CHANNEL 6 W 'T' L309/2/2 to 30.0 60.0 SECONDS 90.0 120.0 150.0 -4.000J 4.000 CHANNEL 5 U ' W L309/2/2 to -4.000J '30.8 ' 60. SECONDS Figure 7b. Time series traces of w'q', w'T', and u'w'. Run 309/2/2, z/L^O.O. 1.000" CHANNEL 7 W Q * L305/1/1 30.0 60.0 90.0 120.0 150 SECONDS -1.000 J -1.000 :HRNNEL 6 V T L305/1/1 60.0 SECONDS 90.0 120.0 150 L305/1/1 -1.000J Figure 7c. Time series traces for w'q', w'T', and u'w'. Run 305/1/1, z/L=0.29. The trace and scale for w'T' i s inverted. 28 4.2 Cospectra of the Transfers of Momentum, Heat, and Moisture The cospectra of the turbulent transfers were computed as described in Appendix I. For each transfer the composite cospectrum for s t a b i l i t y Group I w i l l be presented. To demonstrate the variation with s t a b i l i t y the mean cospectra plus error bars for Gp. I (most unstable), Gp. VI (near neutral) and Gp. VIIIB (most stable) w i l l be compared. 4.2.1 Momentum Transfer Cospectra In Fig. 8 the composite momentum cospectrum for the most unstable group is given. The scatter within a data run and from run to run was higher for this group than any other (except for the low frequency part of the cospectra for very stable conditions). The standard error of the mean, as determined for the data blocks (see Appendix I) i s indicated for a few cospectral estimates on Fig. 8 and is a measure of the variation i n the transfer due to that scale over the length of the data run. These results indicate that, for this s t a b i l i t y group, the momentum transfer can be quite variable in time. The shape of the momentum transfer cospectrum does not change s i g n i f i c -antly as the s t a b i l i t y changes from unstable (z/L ^ -0.5) to near neutral (see F i g . 9). However the peak frequency of the logarithmic cospectrum, nc^(n) = f 4 ( f ) j shifts from near f = 0.06 for z/L -0.5 to near f = 0.2 for z/lfc 0.0. The curves for the other s t a b i l i t y groups were intermediate to those shown. At low f or large scales the cospectral dependency of f is approximately f^*^, being slightly steeper in the near neutral case compared to the most unstable case. The f a l l - o f f at high f is greater than but appears to be less than the f-5/3 suggested by Panofsky and Mares (1968). Because of instrumental response effects i t is not possible to define this 29 1 . 0 - i 0 * * .01A .oo^A mean value fo r A f A V Gp X o 4 0 0 t> c , 0 0 1 o S.G. Of pt .-+ I I I i • a . 0 1 f 1 0 Figure 8. Composite momentum t r a n s f e r cospectrum f o r Gp. I. 1-1 4 c .H .01A 7 - £ Gp I Gp VI Gp VIIIB . 0 0 1 3i • .1 f ID Figure 9. Va r i a t i o n o f momentum t r a n s f e r cospectrum with s t a b i l i t y , 30 f a l l - o f f slope very accurately. The cospectra for stable stratifications are considerably different from those for neutral to unstable stratifications (Fig. 9). The cospectral shape is much narrower and is shifted in peak frequency to near f = 0.8 for z/L about 4. At low f (below f = 0.1) the cospectra were generally positive indicating upward momentum transfer. This feature of the cospectrum chang-ing sign was also evident In the heat flux cospectrum and w i l l be discussed after considering that cospectrum. 4.2.2 Heat Transfer Cospectra The heat flux cospectra (Fig. 10) generally showed much less variation within runs and less scatter in their composite graphs for s t a b i l i t y groups than did either momentum or moisture transfer. The mean curves for Gps. I, VI and VIIIB are represented in Fig. 11. The characteristics of the normal-ized heat flux cospectrum appear to be similar to those for the normalized momentum flux cospectrum for f less than 0.3. For higher f, the heat flux cospectra f a l l off less rapidly than the stress cospectra. However this difference may be due to the instrument response not responding correctly to u fluctuations. The f a l l - o f f is only sli g h t l y faster than f~^/^. For stable stratifications the heat flux cospectrum behaves s i m i l a r i l y to that of momentum transfer. There is a marked s h i f t to higher f with the peak near f = 1.0 for z/L near 4. For these stable stratifications the normalization of frequency by z is probably not correct; L i s a more meaning-f u l length. I t was found that the stable groups, VII, VIIIA, and VIIIB, a l l had regions at small f (large scales) for which the transfers of heat and momentum were upward; since ^^/Ai was always positive and ^T/<^ l i k e l y positive this indicated momentum and heat transfer against their gradients 31 Figure 11. V a r i a t i o n o f heat t r a n s f e r cospectrum with s t a b i l i t y . 32 at these scales. In most cases a changeover frequency, f , could be deter-mined such that for f < f the transfer was mainly upward or variable with f and for f > f the transfer was consistently downward and the cospectra had a consistent shape with less scatter. The value of f c was found to de-crease with z/L. As was suggested by Stewart (1969), in stable stratifications atmospheric i n e r t i a l wave motions w i l l frequently be mixed with turbulence. One way of identifying the presence of wave motions is by examining the w-T coherence-phase relationships. When the w-T coherence is high the phase angle w i l l be either near zero or near 180° for turbulence at these scales but w i l l be near _ 90 for wave motions. Fig. 12 shows the coherence and phase angles as a function of f for three stable runs. Note that the coherence is mainly high but quite variable for f < f c , small for f i b f c and mainly between 0.2 and 0.4 for f ~? f c . The phase angles scattered for f < f c but are usually between 50° and -90° whereas for f ~y f c the phase angles are consistently between t. 150°. This Indicates that for f > f c the fluctuations of w and T are due to turbulence. For f < f c i t seems that there is a mixture of turbulence and wave motions. For the purposes of this study i t was decided to r e s t r i c t attention to that region dominated by turbulence. The fluxes were defined as the integrals between f T = f and b L c fjj 20. However, the sonic anemometer response is valid only to about f = 2 or 3. A small t i l t of the sonic anemometer could introduce an apparent positive u-w correlation. The maximum l i k e l y t i l t was about one degree. I t was found, however, by rotating the coordinates both ways by one degree that t i l t could not account for the positive u-w correlation and the results were thus considered valid. 1.Ch c <- .6 sz 5.4H .2-1 0 1 0 0 i 5 0 0 - 5 0 o * • 3 0 5 / 2 ° 305/3/1 * 3 0 5 / 3 / 2 • 0 .0 o o x x * x 0 .1 f 1 0 C9 a -c-iOOH a, - 1 5 0 -1 6 0 -.1 f 1 0 * * ^ X » * • • ° „ o O o o « o o Figure 12. Coherence and phase angles for three stable runs 34 4.2.3 Moisture Transfer Cospectra The moisture t r a n s f e r cospectra were computed only f o r the unstable through to n e u t r a l cases and f o r wind speeds greater than 2 m s e c - ^ . The moisture t r a n s f e r composite cospectrum f o r Gp.I i s shown i n F i g . 13 and the mean curves f o r Gps. I and VI compared i n F i g . 14. Note that the s c a t t e r of the moisture composite cospectrum i s l e s s than that f o r momentum tr a n s f e r but appreciably more than that f o r heat t r a n s f e r . The moisture t r a n s f e r cospectra have shapes very s i m i l a r to those f o r momentum tra n s f e r throughout the range of f measured. The method of c o r r e c t i n g these cospectra f o r the phase l a g due to the humidiometer intake pipe i s described i n Appendix I I . Despite un c e r t a i n t i e s i n t h i s technique the d i f f e r e n c e i n c o s p e c t r a l shape at high frequencies between the moisture t r a n s f e r cospectra and the heat t r a n s f e r cospectra appears to be r e a l . 4.3 S p e c t r a l C o r r e l a t i o n C o e f f i c i e n t s . The normalized cospectra i n d i c a t e which scales are important i n c o n t r i b -uting to the transfers but the c o r r e l a t i o n c o e f f i c i e n t as a function of f r e -quency i s more u s e f u l i n i n v e s t i g a t i n g how these transfers are taking place. 4.3.1 Momentum Transfer S p e c t r a l C o r r e l a t i o n C o e f f i c i e n t s . In F i g . 15 are the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r momentum tran s f e r f o r Group I. Note that although at large scales the c o r r e l a t i o n c o e f f i c i e n t i s sometimes very large and negative and at other times large and p o s i t i v e these scales do not contribute much to the t o t a l t r a n s f e r because the s p e c t r a l d e n s i t i e s of w, and hence of uw, at those frequency bands are very small. In a d d i t i o n these points at low frequencies are s t a t i s t i c a l l y very u n r e l i a b l e i n that they each have only a few degrees of freedom. Only - O H c 1 - i . 0 1 H .001H no A + • Gp X 4-xx5 1 . 0 1 1 0 Figure 13. Composite moisture t r a n s f e r cospectrum for Gp. I , 1-1 r1 c cr 11 . 0 1 !o5i . 0 1 Gp i :•; Gp VI :E " T .1 f 1 1 0 Figure 14. V a r i a t i o n of moisture t r a n s f e r cospectrum with s t a b i l i t y . 36 1.0-1 . 8 -f) . 6 -. 4 -. 2 -0 -2-1 -.4 G p 69+ A A X • 0+ D + O o — r . V - # • • V •^1 r-ex— — A 1 + + » j T-gV^r 7a H——^—a n y y ZSL . 0 0 1 .01 .1 f .1 -1 1 0 Figure 15. Spectr a l c o r r e l a t i o n c o e f f i c i e n t s f o r momentum tr a n s f e r f o r Gp. I. 1 . 0 - i Gp Gp III G p V * GpVI . + GpVIIIA n G p VIIIB 7 Figure 16. V a r i a t i o n o f momentum t r a n s f e r s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s with s t a b i l i t y . when averaged over several data runs do these points have any significant meaning. For this most unstable group (Fig. 15) there was frequently evidence of upward momentum transfer by eddies of size 200 metres or larger. These estimates are s t a t i s t i c a l l y unreliable but may be associated with organized meso-scale circulations and w i l l require further investigations involving the whole planetary boundary layer. The mean spectral correlation coefficients for Gps. I, III, V, VI, VIIIA and VIIIB are given in Fig. 16. The error limits, indicated for Gps. I, VI, and VIIIB are indicative of those for the other s t a b i l i t y groups. R (f) for near neutral s t r a t i f i c a t i o n , Gp. VI, is a smooth curve increasing with f to a peak near f = 0.02 and then decreasing with f. The rate at which R (f) de-creases with increasing f beyond f about 1.0 may be due to the instrument's u velocity measurement being contaminated by v component. Since the v-w cor-relation is near zero any v contamination w i l l reduce the apparent u-w cor-relation. As the s t r a t i f i c a t i o n becomes more unstable R u w ( f ) generally decreases, although not consistently for Gps. I l l and V, u n t i l for Gp. I R u w ( f ) is for a l l scales significantly less than R (f) for Gp. VI. Note that the largest relative reduction in R u w ( f ) between Gp. VI and Gp. I is for f less than about 0.02 or for scales of about 100 metres or larger. The peak of R u w ( f ) for Gp. I is near f = 0.06 which is higher than" for Gp. VI. This s h i f t (based actually only on one point) of the peak to higher f for increas-ing i n s t a b i l i t y is in the opposite direction to the s h i f t in the peak of the cospectrum. For stable stratifications R u w ( f ) follows the behaviour of the cospectrum and shifts to higher frequencies. For f less than 0.1, R U w ( f ) for Gp. VIIIB was usually positive and the scatter was much larger. 38 4.3.2 Heat Transfer S p e c t r a l C o r r e l a t i o n C o e f f i c i e n t s . The s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r heat t r a n s f e r have l e s s s c a t t e r than those f o r momentum tr a n s f e r , e s p e c i a l l y i n the unstable case ( F i g . 17). The change of R ( f ) with s t a b i l i t y (as shown i n F i g . 18) i s more consistent than f o r momentum tr a n s f e r , e s p e c i a l l y f o r f greater than 0.06. Note that the standard errors of the means f o r f greater than 0.1 were too small to p l o t (except i n stable cases). For the near n e u t r a l group, Gp. VI, excluding the runs with |z/L| <0.01, R ^ f f ) increases with increasing f to a peak near f = 0.02, the same place as R (f) f o r Gp. VI, and then decreases with i n c r e a -sing f . As the s t r a t i f i c a t i o n becomes more unstable R w ^ ( f ) increases at a l l f . The l a r g e s t r e l a t i v e increases are a low f or large scales so that f o r Gps. I and I I I R w^,(f) i s approximately constant with f f o r f l e s s than about 0.06. At higher f the f a l l - o f f has a s i m i l a r slope to that f o r Gp. I. For the stable cases R ™(f) s h i f t s to higher f i n the same manner as did R ( f ) . wTv ' & uwv ' Note that f o r a l l s t a b i l i t y groups R w^,(f) has a s i g n i f i c a n t value to values of f near 10. 4.3.3 Moisture Transfer S p e c t r a l C o r r e l a t i o n C o e f f i c i e n t s . For Gp. I ( F i g . 19) s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t f o r moisture trans-f e r , R W q ( f ) , i s s i m i l a r to that f o r heat t r a n s f e r but i t decreases more r a p i d l y at smaller scales with decreasing f. F i g . 20 compares the values of R W q ( f ) f o r the four unstable to near n e u t r a l s t a b i l i t y groups. Generally there i s a decrease i n R Wq(f) with decreasing i n s t a b i l i t y but there i s a l o t of s c a t t e r to the diagram. The composite p l o t f o r Gp. V, i n p a r t i c u l a r , had a considerable amount of s c a t t e r . The v a r i a t i o n of R W q ( f ) needs f u r t h e r a m p l i f i c a t i o n . Four s p e c i f i c cases (see Table II) grouped into two pair s w i l l be described i n more d e t a i l , 1.0-1 .84 R w T ( f > .6-.4 .2H 0 - .2H - . 4 -' tt • ° » a-* G p TV 4X . 0 0 1 . 0 1 .1 f 1 1 0 Figure 17. Spectral c o r r e l a t i o n c o e f f i c i e n t s f o r heat t r a n s f e r f or Gp. I. 1.0-, G p G p G p V G p V I GpVI I IA » G p VIIIB igure 18. V a r i a t i o n o f heat t r a n s f e r s p e c t r a l c o r r e l a t i c o e f f i c i e n t s with s t a b i l i t y . 1 0 - i , 8 - * V " ; + 0 ; G P i .6-• . 8° _ * 4- *^ 3. o +D a -.2-I — i 1 1 1 .001 .01 . 1 , 1 10 Figure 19. Spectral c o r r e l a t i o n c o e f f i c i e n t s f o r moisture t r a n s f e r f or Gp. I. - . 2 --.4-1 1 1 1 1 1 .001 .01 . 1 , 1 10 Figure 20. V a r i a t i o n of moisture t r a n s f e r s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s with s t a b i l i t y . 41 Table II. Comparison of Correlation Coefficients for Two Pairs of Data. Pair A Pair B L221/2 L222/2 L224/4 1311/2/1 z/L -0.29 -0.28 -0.15 -0.14 u(cm s" 1) 307 297 487 538 r -0.34 -0.30 -0.30 -0.23 uw r 0.52 0.50 0.47 0.43 wT r 0.49 0.25 . 0.49 0.16 wq Note that i n each p a i r of runs the only s t a t i s t i c i n the table which d i f f e r s s i g n i f i c a n t l y i s that of v , the integrated c o r r e l a t i o n c o e f f i c i e n t , which i s wq high and approximately equal to i n one run of each p a i r and small and much l e s s than V f o r the other run i n the p a i r . The s p e c t r a l c o r r e l a t i o n coef-uw r f i c i e n t s R ^ ( f ) and R ^ ^ f ) are p l o t t e d f o r each p a i r of runs i n F i g s . 21 and 22. The T-q c o r r e l a t i o n f o r L221/2 i s more than twice as high as that f o r L222/2 f o r f greater than 0.05. The w-q c o r r e l a t i o n f o r L221/2 i s higher than that f o r L222/2 f o r a l l s c a l e s , except i n a short range near f = 0.1. For p a i r B, s i m i l a r d i f f e r e n c e s are noted although the d i f f e r e n c e s between T-q c o r r e l a t i o n s are not as l a r g e . These r e s u l t s demonstrate the dependence of the t r a n s f e r e f f i c i e n c y f o r moisture transport on the c o r r e l a t i o n between q, which i s an e s s e n t i a l l y passive s c a l a r being transported, and T, the a c t i v e s c a l a r that causes the convective motions and i s highly c o r r e l a t e d with the v e r t i c a l v e l o c i t y f l u c t u a t i o n s . These d i f f e r e n c e s i n the T-q c o r r e l a t i o n must be explained i n terms of inhomogeneities on a l l s c a l e s . The large scale inhomogeneities of the s i t e (the land-sea contrasts) can not explain the d i f f e r e n c e s . For example L221/2 with a high T-q c o r r e l a t i o n and L311/2/1 with a low T-q c o r r e l a t i o n had the same wind d i r e c t i o n (southerly o f f Boundary Bay) while L222/2 and L224/4 had mainly over-land t r a j e c t o r i e s . The small scale inhomogeneities must be asso-c i a t e d with d i f f e r e n c e s i n the surface boundary conditions. August 21st, the day on which L221/2 and L222/2 were made, was a warm, sunny day that followed a few days of l i g h t showers. I f the evaporation rate varied across the grass surface e i t h e r due to d i f f e r e n c e s i n vegetation or d i f f e r e n c e s In moisture supply then small scale inhomogeneities i n both surface temperature and surface moisture would develop during the day. These dif f e r e n c e s would tend to be a n t i c o r r e l a t e d due to cooling caused by evaporation. August 22nd, on 43 1.0-.8-.6-.4-.2-0--,2A -A-i \ v u \ -r • R * Tq wq L 221/2 R L 222/2 R T q • R ^ + .001 .01 T .1 f 1 10 Figure 21. Spectral correlation coefficients for runs 1221/2 and L222/2. 1.0-1 .8-.6-.4 .2H 0 -.2H -.4 o L224/4 R T q o R L 311/^1 R T q • R wq wq .001 .01 .1 f 1 —I 10 Figure 22. Spectral correlation coefficients for runs L224/4 and 1311/2/1. which L22/4 was run, was sunny and windy while August 24th on which L311/2/1 was run was cloudy, cooler and windy. Here one might expect the T-q c o r r e l a -t i o n associated with the meso-scale c i r c u l a t i o n s to also e f f e c t the trans-f e r s . The mean ^ ( f ) over a l l groups f o r unstable s t r a t i f i c a t i o n s i s indicated i n F i g . 23. 4.3.4 Comparison of the S p e c t r a l C o r r e l a t i o n C o e f f i c i e n t s . The r a t i o s of the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s at d i f f e r e n t scales i s a measure of the r e l a t i v e t r a n s f e r e f f i c i e n c i e s at each scale f o r the d i f f e r e n t f l u x e s . The r a t i o s R^CfO/R (f) are shown i n F i g . 24. The r a t i o of near n e u t r a l s t r a t i f i c a t i o n i s indicated with a double l i n e . R e c a l l that R u w ( f ) and R^Cf) f o r near n e u t r a l c o r r e l a t i o n s both had a peak near f = 0.02 and the,same f a l l - o f f with f . However, at the peak R w T ( f ) was about 0.50 while R ( f ) was about 0.43. Hence the r a t i o R _/R ( f ) & 1 . 2 f o r f greater than uwv J wT uwv ' 6 0.02. By f higher than 0.6, R u ( f ) i s decreasing s l i g h t l y more r a p i d l y and i s near zero while R ^ ^ f ) i s s t i l l r e l a t i v e l y l arge. Hence the r a t i o Rw^ ,(f)/ R (f) increases r a p i d l y and i s not w e l l defined. I t i s important to note that Rv/pC^VRuwCf) i s s i g n i f i c a n t l y greater than 1.0 f o r scales smaller than lOOz and that i t s average i s about 1.4. For t h i s near n e u t r a l case (the z/L values of the component runs are -0.03, -0.03, -0.02, 0.04 and 0.08) the e f f e c t s of buoyancy are s t i l l important. In order to i n v e s t i g a t e the e f f e c t s of buoyancy i n more nearly n e u t r a l s t r a t i f i c a t i o n s w i l l require very accurate measuring equipment. Consideration of the r a t i o R w ^ ( f ) / R u w ( f ) f o r exactly n e u t r a l cases i s not worthwhile because no heat t r a n s f e r takes place and occurrances of those conditions w i l l be very rare. As the s t r a t i f i c a t i o n becomes more unstable the r a t i o R ™(f)/R (f) wi uw generally increases. For the most unstable group, Gp.I, the r a t i o averages near three and i s s i g n i f i c a n t l y higher than the value of the r a t i o f o r any 45 .8H 0 J 1 1 i ! 1 .001 .01 . 1 , 1 10 Figure 23. Spectral c o r r e l a t i o n c o e f f i c i e n t s f o r moisture t r a n s f e r averaged over s t a b i l i t y Groups I to VI. 4-i Figure 24. The r a t i o s o f the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r heat t r a n s f e r to those of momentum t r a n s f e r . other s t a b i l i t y groups. These marked increases i n the r a t i o R (f)/R ( f ) wl uw f o r decreasing s t a b i l i t y are due to the fac t that R w T ( f ) increases and R u w ( f ) decreases so that both act to increase the r a t i o . The increase i s la r g e r at both large scales ( f l e s s than 0.01) and at small scales ( f greater than 0.2) than at the intermediate scales. The increases at small scales are somewhat le s s r e l i a b l e because R ( f ) i s small and effected by instrument response and the r a t i o i s poorly defined. The Increases at l a r g e r scales may be a t t r i b u t e d to the e f f e c t s of buoyancy a c t i n g most e f f i c i e n t l y at these l a r g e r s c a l e s . For a strongly convecting regime a high w-T c o r r e l a t i o n would be expected f o r the scales appropriate to those of the buoyant plumes. However the reasons f o r the reduced R (f ) f o r convecting regimes are not so obvious. R e c a l l U w that although the peak of the momentum t r a n s f e r cospectrum s h i f t e d to lower f ( l a r g e r scales) f o r increasing i n s t a b i l i t y , the peak of R (f) s h i f t e d to higher f (smaller scales) and that the l a r g e s t r e l a t i v e reduction i n R ( f ) was f o r large s c a l e s . In a buoyant s i t u a t i o n the large updrafts would o r i g i n a t e near the surface and hence carry a i r with a small h o r i z o n t a l v e l o c -i t y or r e l a t i v e to the mean wind at the observing l e v e l these large p o s i t -ive w f l u c t u a t i o n s would carry large negative u f l u c t u a t i o n s and hence a large amount of momentum would be transported during the updraft. For a constant f l u x l a y e r the amount of momentum t r a n s f e r w i l l be determined near the surface where buoyant forces are not important. Since only a c e r t a i n amount of momen-tum t r a n s f e r i s required the u-w c o r r e l a t i o n between updrafts would be r e l a -t i v e l y low. This implies that the momentum t r a n s f e r should take place i n bursts and would be quite v a r i a b l e during the duration of a data run. These points are i n agreement with observations on the data made e a r l i e r i n t h i s chapter. Thus during a s u f f i c i e n t l y long time i n a f r e e l y convecting regime the same amount of momentum can be transported v e r t i c a l l y at s p e c i f i c scales while the c o r r e l a t i o n c o e f f i c i e n t w i l l be lower than i n neu t r a l c o n d i t i o n s . For the stable case R ,j,(f)/ R u w ( f ) i s not s i g n i f i c a n t l y d i f f e r e n t than unity f o r f<1.0 but appears to be higher f o r f ^1.0. Thus i n the small scale region i n which mechanical turbulence i s believed to dominate the tr a n s f e r mechanism, the e f f i c i e n c y of heat t r a n s f e r i s greater than that o f momentum t r a n s f e r . It has generally been believed that the opposite should be true (Lumley and Panofsky, 1964,p.106). Further i n v e s t i g a t i o n s under a va r i e t y o f conditions are needed to confirm t h i s . 4.4 C o r r e l a t i o n C o e f f i c i e n t s The c o r r e l a t i o n c o e f f i c i e n t s , as defined i n Eq. 2.7, have been averaged over s t a b i l i t y i n t e r v a l s as in d i c a t e d i n Table I. For each point on the graph the v e r t i c a l l i n e represents the standard er r o r o f the mean o f the data averaged to obtain the p o i n t . The l i n e i s p l o t t e d f o r the average z/L value o f the group. The h o r i z o n t a l l i n e shows the s t a b i l i t y range averaged over. Note that the z/L scale i s l i n e a r from -0.7 to 0.1 and i s logarithmic f o r higher values o f z/L. 4.4.1 Momentum Transfer C o r r e l a t i o n C o e f f i e c i e n t s The c o r r e l a t i o n c o e f f i c i e n t , r , ( F i g . 25a) i s negative for a l l z/L and has a value near -0.3 f o r n e u t r a l c o n d i t i o n s . For increasing z/L r ° ' uw decreases approximately l i n e a r l y . For unstable s t r a t i f i c a t i o n s can be represented as r u w = -0.31(1 - 0.661z/L I). This empirical r e l a t i o n and a l l others presented i n t h i s s e c t i o n are l e a s t squares best f i t s to the data. For stable s t r a t i f i c a t i o n s r , when forced to go to -0.31 at z/L = 0, was uw to ' ' r =-0.31(1 - 0.161z/L | ) . Thus the e f f i c i e n c y of momentum t r a n s f e r decreases uw more r a p i d l y f o r i n c r e a s i n g i n s t a b i l i t y than i t does f o r incr e a s i n g s t a b i l i t y . vertical bars arc standard error of mean. 1P1 . 5 -H >• —r -.5 u w —H-+— 6 .1 "1—i—I 1 3 10 Figure 25a. V a r i a t i o n o f the c o r r e l a t i o n c o e f f i c i e n t s f o r momentum t r a n s f e r with s t a b i l i t y . 10n . 5 -i r -.5 WTI -if-z/L 6 .1 \ 3 16 Figure 25b. V a r i a t i o n o f the c o r r e l a t i o n c o e f f i c i e n t s f o r heat t r a n s f e r with s t a b i l i t y . 1.0-» other days Figure 25c. V a r i a t i o n o f the c o r r e l a t i o n c o e f f i c i e n t s f o r moisture t r a n s f e r with s t a b i l i t y . Neither equation can be expected to apply f o r very large values of |z/L|; the l i m i t s being about 0.7 on the unstable side and about 5 on the stable s i d e . The r e s u l t s quoted here f o r unstable s t r a t i f i c a t i o n s agree with those of Haugen et a l (1970) but disagee with those o f Mordukhovich and Tsvang (1966) who found r increased i n magnitude as z/L decreased from zero. This r e s u l t uw ° ' may have been due to nstrumental l i m i t a t i o n s . I f an instrument does not properly measure the high frequency part o f the uw-cospectrum (see F i g . 9) then the er r o r or reduction i n uw would be greatest f o r near n e u t r a l condi-t i o n s and would decrease as z/L decreased. 4.4.2 Heat Transfer C o r r e l a t i o n C o e f f i c i e n t s The magnitude o f the c o r r e l a t i o n c o e f f i c i e n t f o r heat t r a n s f e r , r w r j o as a function o f z/L i s shown i n F i g . 25b. Since z/L i s determined almost e n t i r e l y by the heat f l u x , r ^ i s n a t u r a l l y p o s i t i v e when z/L i s negative and v i c e versa. The magnitude o f r ,^ appears to be a montonically decreasing fu n c t i o n o f z/L. The l e a s t squares best f i t over a l l z/L gave |r = 0.46 (1 - 0.19z/L). The three p o i n t s o f very nearly n e u t r a l s t a b i l i t y (|z/L|<0.01) were excluded from the data used to f i t the curve. Although i s usually considered as being zero f o r z/L = 0, i t must from the point of view o f s i m i -l a r i t y theory be considered as undefined. This i s because f o r n e u t r a l condi-t i o n s meeting the c r i t e r i a o f h o r i z o n t a l homogeneity both w'T' and T^ , would be zero. Hence the empirical r e l a t i o n i s v a l i d f o r z/L near but not exactly zero at which poi n t r w T i s undefined. The range o f a p p l i c a b i l i t y o f t h i s e m p i r i c a l r e l a t i o n i s about the same as that f o r r r uw These r e s u l t s are i n f a i r l y good agreement with those o f Haugen et a l (1970), Wesley et a l (1970), and Mordukhovich and Tsvang (1966). 50 4.4.3 Moisture Transfer C o r r e l a t i o n C o e f f i c i e n t s In s e c t i o n 4.3.3 the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t for moisture t r a n s f e r was shown to depend on the T-q. c o r r e l a t i o n . When averaged over s t a b i l i t y qroups the c o r r e l a t i o n c o e f f i c i e n t , ^ j does show a v a r i a t i o n with z/L s i m i l a r to that f o r r ^ • These averaged values o f r are always l e s s than those o f ^w<£« The s c a t t e r i s also much l a r g e r . For s t a b i l i t y groups IV and V the data could be divided into two groups; those on August 24th and those on the other days. These groups are p l o t t e d separately on F i g . 25c. The "other days" group did have some low values of r (fo r example, 1222/2 discussed i n s e c t i o n 4.3.3) but were generally higher than those o f August 24th. The best f i t to a l l the data was|r w^|= 0.33(1-0.23z/L). Note that the slope o f t h i s l i n e i s not s i g n i f i c a n t l y d i f f e r e n t from that f o r r j . The mean r a t i o o f lrw^/rWq|^s f n u s about 1.4 without much dependence on s t a b i l i t y . The data does i n d i c a t e , though^that for l e s s unstable s t r a t i f i c a t i o n s the l i k e l i h o o d o f r values being d i f f e r e n t from the mean i s higher than f o r more unstable wq cases. 4.4.4 Comparison o f the C o r r e l a t i o n C o e f f i c i e n t s The r e l a t i v e values o f these c o r r e l a t i o n c o e f f i c i e n t s are o f as much i n t e r e s t as t h e i r a c t u a l values. The r a t i o s | r w i > / r u w | a r e p l o t t e d i n F i g . 26. The v a r i a t i o n o f the r a t i o i s quite c o n s i s t e n t . The best l i n e a r f i t i s lr T / r 1= 1.4(1+1.8|z/L|) for unstable c o n d i t i o n s . For stable s t r a t i f i c a t i o n s the r a t i o averages about 1.1 and the v a r i a t i o n with z/L i s small and i n s i g n i f i -cant . The f a c t that the r a t i o i s s i g n i f i c a n t l y greater than unity f o r near n e u t r a l and averages greater than unity f o r stable conditions i s i n contra-d i c t i o n to the generally believed ideas that the mechanisms are s i m i l a r f o r near n e u t r a l and stable s t r a t i f i c a t i o n s (Lumley and Panosky, 1964). 51 4i 34 wT uw — r - ^ — i — i — i O .1 1 3 10 Figure 26. V a r i a t i o n o f the r a t i o o f the c o r r e a l t i o n c o e f f i c i e n t s o f heat t r a n s f e r to those o f momentum t r a n s f e r with s t a b i l i t y . . 52 For unstable conditions the ratios increase at f i r s t r a p i d l y and then l e s s r a p i d l y as z/L decreases from zero. This implies a power law type dependence on z/L. The best f i t o f the data on a l o g - l o g p l o t gave | r W T / r w u ) | =3 \z/L| "5 . This f i t s the data better than a l i n e a r f i t . For the most unstable s t r a t i f i c a t i o n s the e f f e c t s o f buoyancy make the t r a n s f e r e f f i c i e n c y f o r heat t r a n s f e r about 2.7 times that f o r momentum t r a n s f e r . As more buoy-ant energy i s added i t does not seem to increase the comparative e f f i c i e n c y by the same amount. This implies that there i s probably an upper l i m i t on the r a t i o I r ~ / r I wT' uw' The v a r i a t i o n o f l r / r I with s t a b i l i t y i s given i n F i g . 27. The 1 wq' uwl to v a r i a t i o n i s e f f e c t e d by the T-q c o r r e l a t i o n s v a r i a t i o n and the s c a t t e r f o r Gps. IV and V i s very l a r g e . As before, the data from August 24 i n Gps. IV and V are separated from those recorded on other days. The data can be f i t by f rwq^ r uvJ = 0*86(l+2.2|z/L|) f o r z / L l e s s than zero and ] r W q / r u w ( approximately constant, 0.7, f o r z/L greater than zero. The behaviour i s s i m i l a r to that o f lr m / r | but the values are much lower. Since i t has been shown that r wT' uw1 wq depends on the T-q c o r r e l a t i o n and not d i r e c t l y on z/L i t i s not worthwhile pursuing the v a r i a t i o n o f r / r any f u r t h e r . r to wq' uw J 4.5 Consideration o f K^/K^ The r a t i o o f the turbulent d i f f u s i v i t y o f heat t r a n s f e r or o f moisture t r a n s f e r to that o f momentum t r a n s f e r has been widely debated i n the l i t e r a t u r e (see, f o r example, Lumley and Panofsky, 1964). Since neither temperature nor humidity p r o f i l e s were measured i n t h i s study no d i r e c t estimates of or K^ , are p o s s i b l e . However, as was pointed out i n Chapter 2, r u _^ ( ^ 1 ' d2 53 4-| other clays 1-T 1 -.5 T wq uw 0 .1 i—i—i 1 3 10 Aug. 24' i r z/L Figure 27. V a r i a t i o n o f the r a t i o o f the c o r r e l a t i o n c o e f f i c i e n t s of moisture t r a n s f e r to those o f momentum t r a n s f e r with s t a b i l i t y . On Aug. 24th the T-q c o r r e l a t i o n was generally lower than on the "other days". 54 Tsvang ( 1 9 6 0 ) has shown that (J"/z | J i s approximately unity f o r unstable s t r a t i -f i c a t i o n s . This could be expected i f a l l the temperature f l u c t u a t i o n s were created l o c a l l y by the v e r t i c a l . v e l o c i t y f l u c t u a t i o n s a c t i n g on the temperature gradient. Similar arguments would apply to ^ T / z ^ . In F i g . 28, ^ F / z j ^ i s p l o t t e d against z/L. The g r a d i e n t ^ was computed from the best l o g - l i n e a r p r o f i l e f i t to ths data. The r e s u l t s i n d i c a t e that ( T / z ^ i s also approx-imately constant f o r unstable conditions and i t s value i s not too f a r from unity (about 1 . 2 ) . Hence i t can be assumed that the r a t i o ^ " w / ^ ) ^ / 2 ^ ) i s approximately unity over the z/L rang 0 to -0.5 and that rwf/ruw~^H^^Sl* Two recent estimates of the r a t i o K^/K^ have been made. One, due to Swinbank ( 1 9 6 8 ) , l e d to the empirical formula KJJ/K^ = 2.7|z/L| :4 . Unfortunately no d i r e c t measurements of s t r e s s were made and u A was i n f e r r e d from the wind p r o f i l e s . Businger et a l ( 1 9 7 0 ) measured d i r e c t l y both the t r a n s f e r s and the p r o f i l e s . Their measurements were analysed within the framework o f the Businger-Dyer theory (see Paulson, 1 9 6 7 ) and l e d t o : f o r unstable s t r a t i f i c a t i o n s and KJJ/K^ approximately constant (about 1.35) f o r the stable range o f z/L. In F i g . 29 the r e s u l t s o f Swinbank and o f Businger are compared with the r e s u l t s shown here, assuming r w r j i / r u w = KJJ/K^- F ° r stable s t r a t i f i c a t i o n s there i s good agreement that K^/K^ i s approximately constant and greater than unity (between 1.1 and 1 . 4 ) . For unstable s t r a t i -f i c a t i o n s my r e s u l t s are higher than e i t h e r Swinbank's or Businger's but a l l r e s u l t s show that Kjj/K^ increases as i n s t a b i l i t y increases and i n d i c a t e that the rate o f increase decreases as z/L becomes more negative. 56 CHAPTER 5 TURBULENT TRANSFERS DURING BOMEX In t h i s chapter the r e s u l t s of d i r e c t measurements of momentum, heat and moisture t r a n s f e r i n a s u b - t r o p i c a l environment (near Barbados) w i l l be presented. Because these data required s p e c i a l analysis procedures these procedures w i l l be presented f i r s t , i n Section 5.1. In Section 5.2 the turbulent t r a n s f e r s during BOMEX w i l l be compared with one another and i n Section 5.3 the r e s u l t s w i l l be compared with those f o r the Ladner experiment. 5.1 S p e c i a l analysis f o r F l i p Data. The analysis of the F l i p experiment data was complicated by the motion of F l i p and also by the disturbance of the mean flow pattern due to the presence of F l i p . F l i p ' s motion i s p r i n c i p a l l y i n two modes. The f i r s t i s the t i l t i n g about h o r i z o n t a l axes due to the ocean waves while the second i s the r o t a t i o n of F l i p around i t s v e r t i c a l axis due to d i f f e r e n t i a l wind pressures. The l a t t e r proved to be f a r more serious f o r these measurements. F l i p ' s disturbance of the mean flow pattern appears to have resu l t e d i n a mean negative v e r t i c a l wind at the 8 m l o c a t i o n of the sonic anemometer (see F i g . 4). The e f f e c t of F l i p ' s r o t a t i o n s about i t s v e r t i c a l a x i s , when large enough, was to cause the sonic anemometer's h o r i z o n t a l wind channels (channels A and B) to saturate. Since the Lyman-oC humidiometer required the a i r to flow through a s e c t i o n of 1 cm diameter tubing to be sampled i t too would not fu n c t i o n when the r o t a t i o n angle exceeded about 50°. Because of these problems with F l i p ' s r o t a t i o n i t w i l l be very d i f f i c u l t , i f indeed p o s s i b l e , to analyse some of the data. The data analysed f o r t h i s t h e s i s only d e a l t with cases 57 where the r e l a t i v e wind d i r e c t i o n did not exceed + 20° during the run. At the I n s t i t u t e of Oceanography at U.B.C. considerable e f f o r t has gone into studying the momentum tra n s f e r into waves, and a good deal i s known about the c o s p e c t r a l shape (Smith, 1967; Weiler and Burling, 1967). The str e s s cospectrum i s also the spectrum that w i l l be most effected by F l i p ' s motion and flow disturbances. Hence, i f the stress can be made meaningful then the other turbulent t r a n s f e r s ( i . e . , heat and water vapour) w i l l also be meaningful. The e f f e c t s of F l i p ' s motion due to the ocean waves can be seen i n F i g . 30. The e f f e c t s on the u and v spectra are s i m i l a r to the e f f e c t s on the w spectrum. As can be seen the wave spectrum i s very narrow and e f f e c t s only a small band-width of the turbulence spectra. The f a c t that the wave peak appears i n the v spectra indicates that the mean wind d i r e c t i o n and the response of F l i p to the waves were not always i n the same v e r t i c a l plane, at l e a s t f o r the long period waves that influence the spectra. This wave-effect peak i n the spectra i s considered to be due to F l i p ' s response to the waves, and hence to varying the t i l t of the anemometer, rather than due to a d i r e c t wind-wave coupling. The waves at the peak of the spectrum have a period of about 8 seconds and hence a wavelength of about 100 metres. The phase speed of the waves was about 12 m sec and the wind speeds about 6 m sec E l l i o t t (1970) has shown that p o t e n t i a l flow theory, i n cases where u<c, i s a good approximation to the measured r e s u l t s . The wave induced v e l o c i t i e s at a height of 8 metres, can thus be c a l c u l a t e d from p o t e n t i a l flow theory (see Lamb, 1945, Sec. 231). The amplitude of the wave induced v e l o c i t i e s , A, w i l l where f) i s the sea wave amplitude 58 .1" n<f>tn) .01 .001-. 0 0 0 1 -uw i + + -f + . wave effects , + w + + + 4 waves \ .001 .01 f To Figure 30. E f f e c t o f F l i p ' s response to ocean waves on the w-spectrum and uw-cospectrum. The u and v-spectra had peaks s i m i l a r to that observed on the w-spectrum, 59 c i s the sea wave phase v e l o c i t y , k i s the wave number of the sea waves, u i s the mean wind speed, z i s the height above the mean wave surface. For /|= 1 m and k = 0.063 m-"*", and ( 5.1) gives 0.02 m sec Hence the wave induced energy w i l l be of the order 4 x 1 0 m ^ sec; however the observed turbulent v e l o c i t i e s at the wave peak had energy l e v e l s of the order -2 2 - 2 of 2 x 10 m sec . Since the p o t e n t i a l flow estimate of wave induced turbulent energy i s more than an order of magnitude smaller than that observ-ed i t i s believed that the wave peaks i n the v e l o c i t y spectra are due to F l i p ' s motion and would not have been present i f the measurements had been made from a f i x e d platform. Measurements of v e l o c i t y made at IOUBC's f i x e d platform do not show wave peaks at comparable heights ( r e l a t i v e to the wave hei g h t ) . To co r r e c t the s t a t i s t i c s f o r the wave motion a smooth curve was drawn connect-ing the unaffected s p e c t r a l estimates. The i n t e g r a l s under the curves were then recomputed f o r the new s p e c t r a l shape. Since the analysis has been r e s t r i c t e d to cases where the r e l a t i v e wind d i r e c t i o n was not r a p i d i l y changing, the only c o r r e c t i o n necessary was to cor r e c t the spectra f o r l a c k of alignment of the sonic anemometer array into the mean wind. Because a l l three v e l o c i t i e s were measured i t was p o s s i b l e to. do these tensor transformations. The SC0R program (see Appendix I ) computed the mean wind speed and d i r e c t i o n ( r e l a t i v e to F l i p ) f o r each block and the average over the data run. Hence an estimate of the wind d i r e c t i o n variance was r e a d i l y a v a i l a b l e . The ROTATE program was then used to compute the spectra and cospectra f o r the aligned coordinate system from the spectra and cospectra f o r the sonic array coordinates. The aligned coordinate system w i l l have the mean wind vector u* i n i t s x - z plane but not n e c e s s a r i l y along the x a x i s . The transformation equations (Kaimal et a l , 1968) used assume the u i s i n the x - y plane but the error i s n e g l i g i b l e since the t i l t of the coordinates i s l e s s than 15°. The e f f e c t of F l i p obviously al t e r e d the mean flow pattern around the instruments (see Mollo-Chrlstensen, 1969). How i t effected the structure of the turbulence i s not known. As a f i r s t step to c o r r e c t i n g f o r Flip's presence i t seems reasonable to c o r r e c t f o r the r e l a t i v e t i l t of the sonic anemometer to the mean wind speed, i . e . to b r i n g x along u. The r e l a t i v e t i l t was the t o t a l of the angle due to the array not being mounted exactly v e r t i c a l l y and the angle due to the d i s t o r t i o n of the near flow around F l i p i n t i l t i n g the u plane. The obvious technique to c o r r e c t f o r t h i s , to rotate u n t i l w = 0, was not desirable i n t h i s case because of the uncertainty of the zero adjustment of the v e r t i c a l channel of the sonic anemometer. Two other techniques were t r i e d . One was to rotate the coordin-ates to obtain a given c o r r e l a t i o n c o e f f i c i e n t between the low frequency u and w components while the other was to rotate to minimize the low frequency w spectrum. L e t $ be the angle that the measuring instrument coordinate x m, z m are from the true coordinates x, z. The true v e l o c i t i e s u' and w' are r e -l a t e d to the measured v e l o c i t i e s u m and w m by: u' = u m cosY - w"1 sinY t _ m \\ . m . y* w1 = w cos « +• u s i n » which lead to the s p e c t r a l r e l a t i o n s : 4 > m u) = £ M * , « * * £ , U ) V - xC (*) *»**** C fa! - C M « • < t » * *<G*»* '** At low frequencies and assuming small t i l t angle these equations become: 61 4m (*) -i« M -C w < €(*) r ' 4" (*) •>• 4^(n) ^ Hence f o r p o s i t i v e V the measured 0^(f\) w i l l be too negative at low frequencies where 0 u ' u ( n ) i s large and the str e s s i n t e g r a l w i l l probably not be defined f o r periods of about an hour. For high frequencies and small the measured values of each of these spectra i s a good approximation to the true value. In order to c a l c u l a t e the t i l t angle V* f o r these spectra the technique of f o r c i n g the low frequency u and w c o r r e l a t i o n c o e f f i c i e n t to a given value, ^  was used. Smith (1967) used t h i s technique with ^ = -0„5 to c o r r e c t some data and obtained s a t i s f a c t o r y r e s u l t s . Using the approximations appropriate to low frequencies the c o r r e l a t i o n c o e f f i c i e n t can be written as: 4"H («) <• 4UUT(») t h i s can be solved f o r ^  to give I f The value of $ w i l l , of course, be a fu n c t i o n of frequency. The ROTATE progr-am computed the average value of ^ over a band of frequencies. A value of -0.5 was chosen f o r the range from 0.01 Hz to 0.01 Hz. Because of the sc a t t e r of the data f o r R ( f ) , i t was decided to see the e f f e c t s of other uwv J 3 values of j% . The r e s u l t s are given i n F i g . 31 and the i n t e g r a l s summarized i n Table I I I . Note that f o r c o r r e l a t i o n c o e f f i c i e n t s -0.3 the low frequency uw cospectrum i s pushed p o s i t i v e which i s u n r e a l i s t i c . For £ = -0.6 the cospectra has a much wider bandwidth than previous r e s u l t s had indicated. This indicated that -0.5 was a good choice f o r ^  f o r that frequency i n t e r v a l . The other technique t r i e d was minimize the low frequency w spectrum. 0 t was ca l c u l a t e d as: ^wwv + f o r values of K = 0, + 1, -t- 2, + 3, ...,+• ^ m a x where A n a x and A $ could be • - - - _ ~£W s p e c i f i e d . The value of f was found that made the average of 0 (n) over a c ° rwwv ' frequency band a minimum. F i g 31 showed the e f f e c t of doing t h i s over the frequency range f = 0.01 to 0.1 Hz, but the r e s u l t i n g cospectrum became . p o s i t i v e at low f and was considered as unreasonable. I f the length of the data run i s s u f f i c i e n t l y long then there w i l l be a band of very low frequenc-ies (e.g. f = 0.0001 to 0.001 Hz) f o r which t h i s technique i s u s e f u l . For run 14/2 minimizing the 0 ( f ) spectrum a t very low frequencies l e d to a t i l t angle of 11.5 degrees, i n good agreement with the ji - -0.5 technique f o r the same run which gave 12.5 degrees. However, f o r t h i s technique the value of t i s based on s p e c t r a l estimates that are s t a t i s t i c a l l y l e s s r e l i a b l e than any other region of the spectrum. For t h i s reason i t was decided to use the|£--0.5 technique to co r r e c t f o r anemometer t i l t . 5.2 Comparison of the Turbulent Transfers During BOMEX A l l the BOMEX data were f o r unstable s t r a t i f i c a t i o n s . A complete 63 On 1-k uw ( n ) .01 .001-freq band for tilt angle calculation + + * o * > a + * o a o tilt 0. as meas. tilt 9.2 |3=-0 6 tilt 12.5 p =-0 5 tilt 15.0 (3 :-04 tilt 17.5o =-03 tilt 18.5° w min •+ a • _ °: t \ am t t l all pts. approx. - equal I § f£**I>valucs negative .001 .01 .1 f 10 Figure 3 1 . E f f e c t o f t i l t on the uw-cospectrum f o r run B14/2. The angles 9.2 to 17.5 degrees were computed f o r the s p e c i f i e d c o r r e l a t i o n c o e f f i c i e n t over the indicated frequency range. The 18.5 degree t i l t r e s u l t s from minimizing the w-variance i n the same frequency range. TABLE I I I E f f e c t s of T i l t Angle on Drag C o e f f i c i e n t and w variance C o r r e l a t i o n C o e f f i c i e n t T i l t Angle ^ 14/1 14/2 Deg Deg Drag C o e f f i c i e n t 14/1 14/2 xl03 w Variance 1 4 / 1 2 / 2 cm /sec 14/2 0 0 2.8 3.5 1340 1310 -0.6 5.0 - 9.2 2.1 2.2 1240 960 -0.5 8.9 12.5 1.6 1.6 1120 870 -0.4 12.0 15.0 1.3 1.2 1000 810 -0.3 15.0 17.5 1.0 1.2 990 780 w minimized 17.5 18.5 .83 1.0 990 770 For a given s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t the t i l t angles were computed by the ROTATE program. Varying the t i l t angle varied the computed s t r e s s 2 2 and hence the drag c o e f f i c i e n t (defined as C^  = u^ A^Q)* ^ n e w - v a r i a n c e also depends on the t i l t angle used. t a b u l a t i o n i s i n Appendix IV. Because of the high evaporation rates over the su b - t r o p i c a l ocean the co n t r i b u t i o n to buoyancy due to the moisture f l u x term i s very s i g n i f i c a n t . The co n t r i b u t i o n by z/L to z/L (see.Equation 2.6) was equally as important as the co n t r i b u t i o n of z/L^. The r a t i o (z/Lq) (z/Lj) was between 0.6 and 1.3 f o r the f i v e data runs analysed. The v a r i a t i o n of z/L was between -0.08 f o r B14/1 to -0.36 f o r B15/3. The non-dimensional c o s p e c t r a l r e s u l t s f o r momentum, heat, and moisture tran s f e r s are compared i n F i g . 32. Note that the shapes of n0 w^(n) and n 0 Wq( n) are very s i m i l a r ; the shape of n0^(n) however, i s s i g n i f i c a n t l y d i f f e r e n t . The heat f l u x cospectrum i s much narrower i n bandwidth and also extends to higher frequencies. The co s p e c t r a l peaks f o r momentum and moisture t r a n s f e r are between f = 0.03 and f = 0.2 whereas f o r heat t r a n s f e r the cospec-t r a l peaks are near f = 0.3 and well-defined. Before discussing the tr a n s f e r s f u r t h e r i t i s necessary to consider the temperature spectra and the T-q c o r r e l a t i o n functions. The spectra of temperature f l u c t u a t i o n s are presented i n F i g . 33. For comparison purposes an average temperature spectrum from Ladner and the humidity spectra from B0MEX are included. Notice the marked d i s s i m i l a r i t y of the B0MEX temper-ature spectra and e i t h e r the B0MEX humidity spectra or the Ladner temperature spectrum. The B0MEX temperature spectrum has an appearance more s i m i l a r to that of -a v e r t i c a l v e l o c i t y spectrum whereas the humidity spectrum has a shape nearer to that of a l o n g i t u d i n a l v e l o c i t y spectrum. The BOMEX temper-ature variance was contributed almost e n t i r e l y by scales between 30 z and 0.3 z (z i s the height of observation, 8m) whereas f o r humidity there were c o n t r i b u -tions from scales as large as those measured, approximately 3000z. The reason f o r the dominance of these scale temperature f l u c t u a t i o n s may be a t t r i b u t e d to the high degree of organization of convective scales i n the subtropics, 66 1-F n<fWn) ul .01H .1-n0WT(n) w'T1 . O H n(?wq(n) w'q' .01H X o 4° A<* + x o 4 4 4- x y • o A 4 if A A 1 ° 4 X A x »4 • X .001 .01 B 14/1 B 14/2 B 15/1 B 15/2 B 15/3 1 .1 XOA + X 0 * 4 * 0 A f 10 Figure 32. Cospectra o f momentum, heat, and moisture t r a n s f e r f o r the F l i p experiment. 67 .1" .01-.001-.0001-BOM EX CK *4 r f r x10 Ladner 4 _ 2 . ° V * » * % . O * + A A+ BOMEX 0 0 B14/1 * B14/2 • B15/2 * B15/1 o B15/3 * .001 .01 .1 f 1 10 Figure 33. Spectra o f temperature and humidity f l u c t u a t i o n s f o r F l i p experiment. A mean temperature spectrum from the Ladner experiment i s included f o r comparison. The convective elements of scales of a few hundred metres are i n patches separated by l a r g e r areas of descending stable a i r . This descending a i r i s warm, dry and l e s s turbulent and more homogeneous than that i n the convective regions. Hence the temperature f l u c t u a t i o n s w i l l be mainly of scales of the s i z e of or smaller than the convective regions. There i s some evidence of a second peak i n the temperature spectrum of scales of s e v e r a l kilometers which might be associated with the combined system of convective and descending a i r regions. Supporting evidence f o r t h i s explanation i s i n the T-q s p e c t r a l c o r r e l a -t i o n c o e f f i c i e n t s (see F i g . 34). For scales smaller than about lOz temper-ature and humidity had a c o r r e l a t i o n c o e f f i c i e n t of higher than 0.8. The high frequency f a l l - o f f may be instrumental. For scales about lOOOz and l a r g e r the c o r r e l a t i o n c o e f f i c i e n t s are between -0.8 and -1.0. For scales i n between Ripq(f) v a r i e s gradually (but somewhat e r r a t i c a l l y ) between these l i m i t s f o r some runs and abruptly changes f o r other runs. These r e s u l t s i n d i c a t e that at large scales ( s e v e r a l Kilometers) warm a i r i s dry and v i c e versa. At small scales the c o r r e l a t i o n i s warm and wet; cold and dry. These data support the explanation given f o r the temperature spectrum. Further i n v e s t i g a t i o n s i n both space and time w i l l be needed before the phenomenon i s understood. The narrow bandwidth of the temperature spectrum, of course, r e f l e c t s i t s e l f i n the t r a n s f e r s . The heat f l u x cospectrum has a shape s i m i l a r to that of the temperature spectrum. This i s because no matter how large R w f ( f ) happens to be f 0 w T(f) w i l l s t i l l be small i f f0 T T(f) i s small. The s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r B14/1, the l e a s t unstable run, and f o r B15/3, the most unstable run, are shown i n F i g s . 35 and 36. At low frequencies the c o r r e l a t i o n c o e f f i c i e n t s have a large s c a t t e r but above f = 0.01 the data are 69 1.0-1 .8H R T n ( f ) .4-.2-0--.4--.6--.8--1.0-• X X X + * 4 o .001 + o 4 + t 4b .1 f B 14/1 B 14/2 B 15/1 B 15/2 B 15/3 o X 10 Figure 34. Temperature-humidity s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r the F l i p experiment. B14/1 o o o o 0 4 / 2 + .01 .001 .1 f 1 10 + + X o Rwq(f ) R T q ( f ) + X y + o O + O O O Figure 35. Spectral c o r r e l a t i o n c o e f f i c i e n t s f o r run B14/1 1.0-i .8-.6-.4-.2-0-.2-.4-.6-.8-1.0 * „ B15/3 • x „ « > o O O o o + . o o o + o 9 o + + + + * + * X • + X + * + . ° • + *" + + 4 > + + X * I 1 " |S 1 1 I .001 ° • . 1 . 1 10 o + ° o © o o f R T (f) Figure 36. S p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r run B15/3 72 more consistent. The s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t f o r momentum tr a n s f e r i s l a r g e l y determined by the analysis procedure (see Section 5.1). However, f o r f greater than 0.1, R (f) i s approximately independent of t i l t angle. For t h i s reason the values of R (f) are only considered f o r f > 0.1. Note that i n run B14/1 f o r f "^0.2, the three s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s are s i m i l a r , i.e.., R ( f ) i R ^ ( f ) it R ft). For the range f = 0.01 to about ' ' uwv ' wTv ' w q w ° f = 0.2, R W g ( f ) i s greater than R w>p(f). For l a r g e r scales R W g ( f ) and Rw>j>(f) are scattered and tend to have opposite signs. For B15/3 R W g ( f ) i s greater than Rw.j.(f) over the range of f from 0.01 to 0.1. The value of R u w ( f ) i s the same as both R^ C f ) and R w (f) f o r f greater than 1.0 but i s generally lower than both f o r f between 0.1 and 1.0. Over most of the range of f f o r which there i s appreciable heat t r a n s f e r , the w-T c o r r e l a t i o n i s s i m i l a r to the w-q c o r r e l a t i o n . Over the same range of f space there are s i g n i f i c a n t temperature f l u c t u a t i o n s ( F i g 33) and the T-q c o r r e l a t i o n i s high ( F i g . 34). For scales between f = 0.01 and f = 0.1 the temperature spectrum i s decreasing with decreasing f and the T-q c o r r e l a t i o n i s also decreasing. I t thus appears that the tr a n s f e r mechanisms f o r heat and moisture t r a n s f e r s are s i m i l a r over the range of f where temperature f l u c t u a t i o n s are con t r i b u t i n g to the buoyancy. For l a r g e r scales the buoyancy i s mainly due to humidity f l u c t u -ations because the temperature f l u c t u a t i o n s are small i n magnitude. For these scales the T-q c o r r e l a t i o n i s smaller and the tr a n s f e r e f f i c i e n c y of moisture t r a n s f e r , as gauged from R ^ f f ) i s greater than that due to heat t r a n s f e r . The r e s u l t s f o r R u w ( f ) Indicate that momentum t r a n s f e r f o r small scales ( f less than 1.0) i s as e f f i c i e n t as e i t h e r heat or moisture t r a n s f e r . Because the observation l e v e l a t BOMEX was four times as high as at Ladner the sonic anemometer response to u f l u c t u a t i o n s i s not as important. 73 5.3 Turbulent Transfers: BOMEX and Ladner The turbulent t r a n s f e r s at BOMEX d i f f e r from those at Ladner p r i m a r i l y f o r two reasons. During BOMEX the moisture f l u c t u a t i o n s were large enough to be equally important with temperature f l u c t u a t i o n s i n causing buoyancy. Secondly the organized convective systems at BOMEX led to a quite d i f f e r e n t d i s t r i b u t i o n with scale of the temperature variance from that observed at Ladner. The r e s u l t was that the Important scales c o n t r i b u t i n g to the heat t r a n s f e r were quite narrow during BOMEX as compared to Ladner; at BOMEX the range was f = 0.03 to f = 3 whereas at Ladner the range was f = 0.001 to f = 3 or 4. The scales c o n t r i b u t i n g to the moisture and momentum t r a n s f e r , from f about 0.001 to f about 1.0, were not s i g n i f i c a n t l y d i f f e r e n t between BOMEX and Ladner. The moisture t r a n s f e r e f f i c i e n c y was, however, equal to that f o r heat t r a n s f e r as a consequence of the f a c t that moisture was import-ant i n c o n t r i b u t i n g to buoyancy. The BOMEX r e s u l t s agreed with the f i n d i n g s from Ladner that the parameter that causes buoyancy w i l l have a high tr a n s -port e f f i c i e n c y . These s u b t r o p i c a l r e s u l t s from BOMEX w i l l have to be v e r i f i e d by many f u r t h e r i n v e s t i g a t i o n s but they do point out some of the features to look f o r . 74 CHAPTER 6 SUMMARY The turbulent fluxes of momentum, heat and moisture, t h e i r s i m i l a r i t i e s and the e f f i c i e n c i e s of t h e i r t r a n s f e r s were examined. The c o s p e c t r a l analyses Indicated that the dominant contributions to the fluxes of momentum, heat, and moisture at Ladner l i e i n the na t u r a l frequency range f = 0.001 to f = 5.0 f o r near n e u t r a l and unstable conditions. The c o s p e c t r a l shapes of a l l three t r a n s f e r s are s i m i l a r f o r f l e s s than 0.3 but the heat f l u x may f a l l o f f l e s s r a p i d l y at high f . The peaks of the cospectra s h i f t from near f = 0.2 f o r near n e u t r a l s t r a t i f i c a t i o n s to near f = 0.06 f o r z/L -0.5. For stable s t r a t i f i c a t i o n s the cospectra show marked s h i f t s to higher n a t u r a l frequency. I t was also shown that atmospheric i n e r t i a l wave motions can be important. The s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s were considered to be a measure of the t r a n s f e r e f f i c i e n c y as a fu n c t i o n of scale s i z e . For momentum t r a n s f e r the e f f i c i e n c y , R u w ( f ) , decreased at a l l scales as i n s t a b i l i t y decreased and the l a r g e s t r e l a t i v e changes were at low frequencies. The heat t r a n s f e r s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s , R w,j,(f), increased at a l l scales as i n -s t a b i l i t y increased. The r a t i o s j R w ^ ( f ) / R u w ( f ) | were greater than 1 f o r i most scales even f o r near n e u t r a l conditions. For more unstable conditions the r a t i o was between 2 and 3. These r e s u l t s indicated that even f o r near n e u t r a l conditions that the t r a n s f e r mechanisms were not the same. I t appears that only the s l i g h t e s t amount of buoyancy (jz/L| 4-0.02 or perhaps smaller) i s needed to make the tr a n s f e r e f f i c i e n c y f o r heat transport more e f f i c i e n t than that f o r momentum transport. 75 As z / l _ decreases from zero the tr a n s f e r e f f i c i e n c y of momentum tr a n s f e r decreases. I t was postulated that t h i s was due to greater amounts of momentum being transferred i n bursts of short duration thus making the s p e c t r a l c o r r e l a -t i o n c o e f f i c i e n t f o r momentum tr a n s f e r , averaged over s u f f i c i e n t time, smaller. The r a t i o of the c o r r e l a t i o n c o e f f i c i e n t s c a l c u l a t e d from the complete data si g n a l s could be approximated by ( | r w ^ / r u w l ) = 3 |z/LJ3 f o r unstable conditions and a constant, about 1.2, f o r stable conditions. The e f f i c i e n c y of moisture t r a n s f e r , when moisture i s a passive s c a l a r , was found to depend on the c o r r e l a t i o n between moisture f l u c t u a t i o n s and those of temperature, which i s the act i v e s c a l a r . These r e s u l t s i n d i c a t e that u n i v e r s a l r e l a t i o n s h i p s p e r t a i n i n g to the tra n s f e r of passive s c a l a r s are u n l i k e l y and that the tr a n s f e r mechanism w i l l depend on both the surface boundary conditions and the lar g e r scale c i r c u l a t i o n s which e f f e c t the pas-si v e s c a l a r - a c t i v e s c a l a r c o r r e l a t i o n . The r e s u l t s from BOMEX pointed out the large d i f f e r e n c e s i n the d i s t r i b u -t i o n of temperature variance at large scales between the subtropics and mid-latitudes. Further the contributions to buoyancy due to humidity were s i g n i f i c a n t a t BOMEX and t h i s i s r e f l e c t e d i n the t r a n s f e r mechanisms. Whereas humidity and momentum transport were by scales between f = 0.001 and f = 1 (as at Ladner), the heat t r a n s f e r was confined wi t h i n the narrow band between f = 0.03 and f = 5. -76 BIBLIOGRAPHY Blackman, R. B., and J . W. Tukey, 1958: The Measurement o f Power Spectra. New York, Dover, 190 pp. Businger, J . A., M. Miyake, A. J . Dyer, and E. F. Bradley, 1967: On the d i r e c t determination of the turbulent heat f l u x near the ground. J . Appl. Meteor., 6, 1025-1032. Businger, J . A., J . C. Wyngaard, Y. Izumi, and E. F. Bradley, 1970: F l u x - p r o f i l e r e l a t i o n s h i p s i n the atmospheric surface l a y e r , (sub-mitted to J . Atmos. S c i . ) . Dyer, A. J . , 1965: The flux-gradient r e l a t i o n f o r turbulent heat t r a n s f e r i n the lower atmosphere. Quart. J . R. Meteor. S o c , 91, 151-157. , 1967: The turbulent transport of heat and water vapour i n an unstable atmosphere. Quart. J . R. Meteor. Soc,£3, 501-508. El d e r k i n , C. E., 1968: Experimental i n v e s t i g a t i o n of the turbulence structure i n the lower atmosphere. AEC Research and Development Report, BNWL-329, B a t t e l l e Memorial I n s t i t u t e , Hanford, Wash. E l l i o t t , J . A., 1970: Microscale pressure f l u c t u a t i o n s measured within the lower atmospheric boundary l a y e r . Ph.D. D i s s e r t a t i o n , Univ. o f B r i t i s h Columbia. \ • Francisco, C. C , and D. J . Beaubian, 1965: An automatic dew poin t hygrometer with thermoelectric c o o l i n g . Humidity and Moisture, _I, Reinhold Publ. Co., New York, 165-173. Garratt, J . R., 1969: Spectral and bulk p r o p e r t i e s of turbulence i n the surface l a y e r o f a i r over the sea. Ph.D. D i s s e r t a t i o n , Univ. o f London. Garrett, J . F., 1970: F i e l d observations of frequency domain s t a t i s t i c s and nonlinear e f f e c t s i n wind-generated ocean waves. Ph.D. D i s s e r t a t i o n , Univ. o f B r i t i s h Columbia. H a l t i n e r , G. J . , and F. L. Martin, 1957: Dynamical and P h y s i c a l Meteorology. New York, McGraw-Hill, 470 pp. Haugen, D. A., J . C. Kaimal, and E. F. Bradley, 1970: An experimental study o f Reynolds s t r e s s and heat f l u x i n the atmospheric surface l a y e r , (submitted to Quart. J . R. Meteor. Soc.). Kaimal, J . C , and J . A. Businger, 1963: A continuous-wave sonic anemometer-thermometer. J . Appl. Meteor., 2^ , 156-167. , J . C. Wyngaard, and D. A. Haugen, 1968: Deriving power spectra from a three-component sonic anemometer. J . Appl'. Meteor., 1_, 827-837. 77 Kuettner, J.P., and J . Holland, 1969: The BOMEX p r o j e c t . B u l l . Amer. Met. S o c , 50, 394-402. Kukharets, V.P., and L.R. Tsvang, 1969: Spectra of the turbulent heat f l u x i n the atmospheric boundary l a y e r . Isv., .Atmos. Oceanic Phys., 5_, 1132-1142. Lamb, H., 1945: Hydrodynamics, New York, Dover, 738 pp. Laufer, J . , 1954: N a t l . Advisory Comm. Aeronaut. Tech. Repts. No 1174. Lumley, J.L., and H.A. Panofsky, 1964: The Structure of Atmospheric Turbulence. New York, Interscience, 239 pp. Mitsuta, Y., 1966: Sonic anemometer-thermometer for general use. J . Meteor. Soc. Japan, 44, 12-23. Miyake, M., R.W. Stewart, and R.W. Bur l i n g , 1970: Spectra and cospectra of turbulence over water. Quart. J . Roy. Meteor. S o c , £6, 138-143. Mollo-Christensen, E , 1969: Wind tunnel t e s t o f the superstructure of R/V F l i p f o r assessment of wind f i e l d d i s t o r t i o n . Rep. 68-2, F l u i d Dyn. Lab., M.I.T., 31 pp. Monin, A.S., and A.M. Obukhov, 1954: Basic laws of turbulent mixing i n the ground l a y e r o f the atmosphere. Akad. Nauk SSSR Geotiz. Inst. Trudy, 151, 163-187. Mordukhovich, M.I., and L.R. Tsvang, 1966: Di r e c t measurements of turbulent flows at two heights i n the atmospheric ground l a y e r . Izv. Atmos. Oceanic Phys., 2, 786-803. Panofsky, H.A., and E. Mares, 1968: Recent measurements of cospectra f o r heat-flux and s t r e s s . Quart. J.R. Meteor. S o c , 94, 581-585. Paulson, C.A., 1967: P r o f i l e s o f Wind Speed, Temperature and Humidity over the Sea. Ph.D. D i s s e r t a t i o n , Department of Atm. S c i . , Univer. o f Wash., Se a t t l e , .128 pp. Phelps, G.T., S. Pond, and U. Gorner, 1970: Simultaneous measurements of humidity and temperature f l u c t u a t i o n s . J . Atmos. S c i . , 27_, 343-345. P h i l l i p s , O.M., 1966: The dynamics of the upper ocean. Cambridge, Cambridge Un i v e r s i t y Press, 277 pp. Pond, S., 1965: Turbulence Spectra i n the Atmospheric Boundary Layer over the Sea. I n s t i t . of Ocean., Univ. of B r i t i s h Columbia, Report No. 19. Randal, D.L., T.E. Hanley, and O.K. Larison, 1965: The NRL Lyman-oo. humidiometer. Humidity and Moisture, I, Reinhold Publ. Co., New York, 444-454. Rudnick, P., 1964: F l i p : an oceanographic buoy. Science, 146, 1268-1273. 78 , 1967: Motion of a large spar buoy i n sea waves. J . Ship Research, 11, 257-267. Smith, S.D., 1967: Thrust-anemometer measurements of wind-velocity spectra and o f Reynolds st r e s s over a c o a s t a l i n l e t . J . Marine Res., 2_5, 519-532 . Stewart, R.W., 1969: Turbulence and waves i n a s t r a t i f i e d atmosphere. Radio Science, 4, 1269-1278. Swinbank, W.C., 1968: A comparison between p r e d i c t i o n s o f dimensional analysis f or the constant-flux layer and observations i n unstable c o n d i t i o n s . Quart. J.R. Meteor. S o c , 94, 460-467. , and A.J. Dyer, 1967: An experimental study i n micro-meteorology. Quart. J.R. Meteor. S o c , 93, 494-500. Taylor, G.I., 1954: The dispersion of matter i n turbulent flow through a p i p e . P r o c Roy. S o c , A, 223, 446-468. Tsvang, L.R., 1960: Measurements of temperature pulse frequency spectra i n the surface l a y e r o f the atmosphere. Izv. ANSSSR, Geophys. Ser. S. 1252. Weiler, H.S., and R.W. Burling, 1967: Di r e c t measurements o f st r e s s and spectra o f turbulence i n the boundary l a y e r over the sea. J . Atmos. S c i . , 24, 653-664. Wexler A, (ed.), 1965: Humidity and Moisture, Reinhold Publ. Co., New York. Zubkovsky, S.L., and B.M. Koprov, 1969: Experimental i n v e s t i g a t i o n o f the spectra o f turbulent heat and momentum fluxes i n the atmospheric surface l a y e r . Isv., Atmos. Oceanic Phys., 5^ 323-331. APPENDIX I SPECTRAL ANALYSIS A l l the data were c o l l e c t e d i n analog form and a l l analysis was done d i g i t a l l y . The analog to d i g i t a l conversion was done using a converter designed and b u i l t at IOUBC. The converter gives 10 b i t s r e s o l u t i o n f o r 10.24 v o l t s f u l l s c a l e input, i . e . 10 mv r e s o l u t i o n . The usual procedure was to simultaneously d i g i t i z e ten channels of information. In the mode of operation used the ten channels were sampled s e q u e n t i a l l y with a 45 microsecond delay between channels. These "cross-channel sequences" were repeated at the rates given i n Table TV. The analog s i g n a l s were reproduced at tape speed 60 inches sec--'- (except Type I which was at 30 ips) to reduce the time required to d i g i t i z e a data run. For Type I the r a t i o of the time between sampling channels to the time between cross channel sweeps i s at most 1:17. The corresponding r a t i o s f o r Types II and I I I were: 1:12; and 1:18. Before d i g i t i z i n g , a l l data were passed through a matched set of l i n e a r phase s h i f t f i l t e r s with a gain of -3db at 160 Hz i n 'reproduce' time, with f a l l - o f f of 12 db per octave. This re s u l t e d i n r e a l time high frequency c u t o f f s at: 40 Hz f o r Type I; 20 Hz f o r Type I I ; and 5 Hz f o r Type I I I . In a l l analyses the s p e c t r a l estimates were corrected f o r attenu-a t i o n by the f i l t e r s . The output of the A-D converter was relayed to a C o n t r o l Data Corp "8092 Teleprogrammer" (a small computer) which wrote the data onto a 7 track d i g i t a l tape i n a format that could be read on the IBM 360/67 of the UBC Computing Centre which was used to do the a n a l y s i s . The IOUBC s p e c t r a l analysis system i s outlined i n F i g . 37. The programs TVERIF, FTOR, and SC0R were developed by two other graduate 80 Table IV. D i g i t a l Sampling Frequencies. I Ladner data (except i n II) II Ladner 216,219,220,221,222. II I F l i p data Real Time 80 Hz 60 Hz 20 Hz Playback Time 320 Hz 480 Hz 640 Hz A/D CDC 8092 TV ERF preli mi nary spectra normal ized spect ra Tape Figure 37. IOUBC s p e c t r a l analysis system. students, Dr. J.F. G a r r e t t and J.R. Wilson. The author's contributions were the ROTATE and SIMPLOT programs and modifications to SCOR. The TVERIF or tape v e r i f y program was used to check the d i g i t a l tape f o r e r r o r s . The technique used f o r t h i s thesis was compute the F o u r i e r c o e f f i c i e n t s of the time s e r i e s by use of a " f a s t " F o u r i e r transform (FFT) subroutine (see IEEE Transactions on Audio and E l e c t r o - a c o u s t i c s , June, 1967) and then compute the spectra and cospectra from these c o e f f i c i e n t s . The d e t a i l s of t h i s procedure have been given by Garrett (1970)« The FTOR program computed the F o u r i e r c o e f f i c i e n t s f o r data blocks containing 1024 samples from each of the ten channels. The SCOR program computed from the c o e f f i c i e n t s the required spectra and cross spectra. These s p e c t r a l estimates were averaged over approximately one-eighth decade frequency bands. For a t y p i c a l Ladner data run, there was enough data f o r 64 data blocks. The range of frequency analysis was from n-j_ = 1 /w&r= 0.078 Hz and At i s the time between samples (=0.0125 s e c ) , to n w = 40 Hz. This lower frequency l i m i t , n^ was too high to include a l l the low frequency energy f o r some v a r i a b l e s . Hence a procedure was developed to extend the a n a l y s i s to lower frequencies while at the same time not unduly extending the analyses procedure. In computing the F o u r i e r c o e f f i c i e n t s f o r each block the average value of each s i g n a l over that block i s automatically computed. These block averages (u s u a l l y 64 i n number) then c o n s t i t u t e a new time s e r i e s . The SCOR program was modified to include a small FTOR-like program to compute the F o u r i e r c o e f f i c i e n t s of t h i s new time s e r i e s . The band-averaged spectra and cross spectra f o r t h i s new time s e r i e s were computed i n SCOR i n exactly the same manner as the others. The r e s u l t a n t new spectra are the same as i f the time s e r i e s had been "box car" averaged over 1024 data points and then sampled every 1024th point. The e f f e c t of 83 the box car average i s to modify the spectrum with a sinc2 f u n c t i o n ; i . e . the s p e c t r a l estimates are m u l t i p l i e d by 'if(n) where: 1 2 tin) = S-nnr/&TU\T I _ S i n c " (jrm) j where T i s the length of the average. How t h i s a f f e c t s the data w i l l now be investigated. For a t y p i c a l Ladner case T was 12.8 seconds. The t r a n s f e r f u n c t i o n t (n) i s given i n F i g . 38. Taking every 1024th point has the e f f e c t of a l i a s i n g the data or f o l d i n g 'fc'(n) * <j> (n) around the Nyquist frequency which i n t h i s case was = 1/2T. The folded (n) i s also shown i n F i g . 38. I f n<j>33(n)cxn at low frequencies (see Miyake et a l , 1970) then ^ ^ ( n ) = constant f o r low n and the e f f e c t of the t r a n s f e r f u n c t i o n i s to d i s t o r t the spectrum as shown. Also shown i s the r e s u l t f o r (j)(n)°<n-l, The s p e c t r a l window f o r the low frequency analysis reduces the s p e c t r a l energy density to 80% of i t s value at n^y. The t y p i c a l value of n^y was 0.039 Hz which f o r z = 2m and u = 4 m/s gives f = nz/u = 0.02. According to Miyake et a l (1970) l e s s than 20% of the momentum t r a n s f e r occurs f o r f < 0.02. From the same data (Miyake et a l , 1970; Weiler and Bu r l i n g , 1968) the contributions to <F f o r f < 0.02 are n e g l i g i b l e . Hence although the t r a n s f e r f u n c t i o n t ( n ) e f f e c t s the s p e c t r a l shape, the e f f e c t on the t r a n s f e r s i s l i k e l y to be small. The n a t u r a l s c a t t e r of the s p e c t r a l estimates tends to conceal the t r a n s f e r f u n c t i o n e f f e c t s . In F i g . 39 values of log n<^w(n)/g-2 f o r one run, computed by three separate techniques, are p l o t t e d . One method was the FFT technique used i n . t h i s t h e s i s . The second was by standard analog computer techniques on the I0UBC analog computer. The t h i r d was also an analog computation but done by the Soviet s c i e n t i s t s of the I n s t i t u t e of Physics of the Atmosphere, Moscow (see Kukharets and Tsvang, 1969). The data run Figure 38.. The low frequency analysis t r a n s f e r function and i t s e f f e c t on s p e c t r a . oo 0.1 H V 0.0H o o digital low i frequency 4 I ^ analysis 0 ' o + o + o +• o + 3 + o o Digital + Analog U.B.C. Analog I.RA.US.SR 0.01 0.1 1 10 n Figure 3 9 . Comparison o f three s p e c t r a l a n a l y s i s techniques. 00 cn 86 analysed was c o l l e c t e d during an IOUBC - I.P.A. "Instrument Inter-comparison" and i s not included amongst those analysed f o r t h i s t h e s i s . The agreement i n the s p e c t r a l shapes i s very good. A f o r t y minute s e c t i o n of data (also c o l l e c t e d during the IOUBC - I.P.A. comparison) was d i g i t i z e d twice, once at 10 samples/sec and once at 60 samples/sec. The l o n g i t u d i n a l v e l o c i t y spectra are compared i n F i g . 40; Because of the d i f f e r e n c e i n d i g i t i z i n g rates the low frequency analysis begins at d i f f e r e n t places and i t s e f f e c t can be compared with the regular a n a l y s i s . The h o r i z o n t a l bars represent the bandwidth over which each s p e c t r a l estimate applies. The v e r t i c a l bars represent the 80% confidence l i m i t s computed from the deviations of the estimates from block to block. For the low frequency analysis no such error estimates are a v a i l a b l e because these are only one block. However, an estimate of the v a r i a t i o n can be obtained by computing the confidence l i m i t s based on the number of degrees of freedom of each s p e c t r a l value (which, i n t h i s case, i s the number of harmonics averaged over i n the bandwidth). The eighty per cent confidence l i m i t s based on the number of degrees of freedom (Blackman & Tukey, 1958, p.22) are p l o t t e d f o r the low frequency estimates. The r e s u l t s of both analyses agree w e l l w i t h i n t h e i r expected error l i m i t s . These r e s u l t s i n d i c a t e that the low frequency analysis technique i s s u i t a b l e f o r the type of analysis required. The ROTATE program was used to convert the spectra and cospectra from the somic anemometer coordinate system ( i . e . from two h o r i z o n t a l paths at 120° separation) to the normal x, y, z coordinate system with x i n the mean wind d i r e c t i o n and z v e r t i c a l . The equations used have been given by Kaimal et a l (1968). The SIMPL0T was developed to present spectra i n convenient normalized forms. The outputs were both i n the form of printed output and 1-3 3 c .1" .01--1 — _ l X- + +4 low frcq. analysis 10 Hz low frcq. analysis 60 Hz / 80% confidence limits bandwidth .001 —r~ .01 .1 00 Figure 40. Check on low frequency analysis by comparing overlap o f analysis regions, g r a p h i c a l p l o t s . Since each s p e c t r a l estimate was the average of estimates from each o f the blocks of data i t was po s s i b l e to calculate' the standard error o f the average as: ' i . x where 4>J (n) i s the s p e c t r a l estimate f o r the j t h data block 4? (n) i s the average estimate f o r the t o t a l length o f the run N i s the number o f data blocks (normally 64). The standard error of the mean i s thus a measure o f the v a r i a t i o n o f the s p e c t r a l estimate f o r a given frequency n. When computing the average co-spectrum or s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r a s t a b i l i t y group the standard error o f the mean was computed as: where <p (n) i s estimate f o r frequency n f o r the k t h run i n the s t a b i l i t y group § (n) i s the average estimate f o r the group M i s the number o f runs averaged (usually 7 ) . This standard error was p l o t t e d on the graphs o f cospectrum or s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s v a r i a t i o n with s t a b i l i t y . 8 9 APPENDIX II HUMIDITY ANALYSIS In measuring the humidity f l u c t u a t i o n s i t was necessary to use a 0.65 m long tube through which the a i r to be sampled passed. This had two major e f f e c t s on the data. The' f i r s t was to introduce a phase l a g between the humidity f l u c t u a t i o n s and the v e r t i c a l v e l o c i t y and temperature f l u c t u a t i o n s . The second was that the tube turbulence damped out the small scale atmos-pheric humidity f l u c t u a t i o n s . The simplest approach to the phase l a g problem was to assume some advection v e l o c i t y through the pipe. U p , and set the time lag'tp = L/up where L i s the length of the pipe. This i s s u r e l y an over-s i m p l i f i c a t i o n but any more complicated c o r r e c t i o n would have required a d e t a i l e d i n v e s t i g a t i o n of the pipe flow which was not f e l t to be j u s t i f i e d . To determine u , the tube and humidiometer were exposed to a wind i n a s i m i l a r experimental set-up as used during the measurements. A hot wire anemometer was used to measure the mean wind speed at the centre of the pipe near the emitter-detector tubes of the humidiometer. The measured speeds were assumed to be representative of U p . In mean wind speeds u ranging from 2 to 4 m/sec, the r a t i o U p / u scattered between 0.24 and 0.41 with no apparent wind speed dependence. Hence U p = u/3 was assumed to be a reasonable value f o r a l l wind speeds. In computing the cospectrum of humidity and any other v a r i a b l e ( u s u a l l y v e r t i c a l v e l o c i t y ) the cospectrum was corrected by the r a t i o cos( c£ - 2 TTn /^)/cos ^ where J i s the phase angle and 2TT"nt:= 2~fr nL/ U p i s the c o r r e c t i o n due to the pipe. No c o r r e c t i o n s were attempted beyond 2 T t n t = 2TT because the humidity f l u c t u a t i o n s of higher frequencies were being damped out by the mixing i n the pipe. The e f f e c t of the phase c o r r e c -tions was to r a i s e the w'q' c o r r e l a t i o n c o e f f i c i e n t to nearly the value of 90 the coherence. In the measurement of atmospheric humidity i t i s always d i f f i c u l t to determine the c a l i b r a t i o n of any sensor. The dew point hygrometer used i n t h i s experiment has the advantage that i t s c a l i b r a t i o n depends on the c a l i b r a -t i o n of a platinum res i s t a n c e thermometer which i s comparatively easy to determine. This assumes, of course, that the dew point mirror i s at the dew point temperature when dew forms on i t ; although contamination may have an e f f e c t i t w i l l be assumed that t h i s i s true. The Lyman-(X humidiometer, on the other hand, has to be compared with another sensor that also measures humidity. The procedure adopted.in t h i s t h e s i s was to f i e l d c a l i b r a t e the humidiometer against the dew point hygrometer by running both instruments simultaneously during the experiment and comparing t h e i r low frequency s p e c t r a l values. The following approximation was developed to obtain humidity f l u c t u a t i o n s i n terms of dew point temperature f l u c t u a t i o n s . The basic equation i s the Clausius-Clapeyron equation, ( f o r example, H a l t i n e r and Martin, 1957, p. 23) I d € 5 _ Lj^ 2. where e g i s the s a t u r a t i o n vapour pressure T i s the absolute temperature i s the l a t e n t heat of vapo r i z a t i o n R v i s the p e r f e c t gas constant f o r water vapour. Both and can be assumed constant over the range of temperatures con-sidered. This equation i s equally v a l i d f o r r e l a t i n g e, the actu a l vapour pressure, and T^, the dew point temperature. S u b s t i t u t i n g e f o r e g and T,j f o r T and i n t e g r a t i n g from T = 273° K to T gives: \n e - U e0 = Uv- / _J± 91 or U e - 1-81 + I V I The r e l a t i o n s h i p between s p e c i f i c humidity q and vapour pressure e i s : p - e Further making the s u b s t i t u t i o n q = q - q' and T, = T, - T,, leads to: I f the average of t h i s equation i s subtracted from i t , then to f i r s t order i n meter measurements. A l i n e a r approximation r e l a t i n g voltage f l u c t u a t i o n to humidity f l u c t u a t i o n was assumed f o r the Lyman-o< humidiometer. Pond (person-ne l communication) has shown t h i s to be v a l i d f o r t y p i c a l atmospheric humidity f l u c t u a t i o n s . The spectra of the dew point hygrometer s i g n a l and the simul-taneous humidiometer s i g n a l are shown i n F i g . 41. The spectra compare very w e l l up to f = 0.1.; at higher frequencies the response of the slower dew-point hygrometer f a l l s o f f . I t i s believed that the f a l l - o f f with frequency of the Lyman-OJ humidio-meter output was due to increased mixing i n the intake tubes. Taylor (1954) has determined the c o e f f i c i e n t of mixing of matter i n turbulent flow i n a The mean q and T a were determined f o r each run on the basis of s l i n g psychro-92 1 O-i 1-•1-.01-Ly-(X humidiometer + Dew pt hygrometer • • ^ + 4-+ t run L 300/1 .001 .01 f 10 Figure 41. Comparison o f s p e c t r a l estimates o f Lyman- o< humidiometer and dew point hygrometer. 93 tube. Although the r e s u l t s are not exactly applicable because of length/ diameter r a t i o of the humidiometer tube was only 20 (compared to sev e r a l hundred f o r Taylor's measurements) some idea of the e f f e c t s of mixing can be obtained. Taylor showed that K = 10.1 au( "*) where K i s the " v i r t u a l u c o e f f i c i e n t of mixing", a, the radius of the tube, and u the mean flow speed. For flow i n smooth pipes (again when length/diameter i s large enough) u A / u depends only on the Reynolds number. For run 300/1, the pipe Reynolds number, Re ^ 4 x 10 3 and hence u/ u* ^  14 which gives K -~200. The P r a n d t l Number I'/K, i s thus about I O - 3 . For flows at low P r a n d t l Number the spectrum of a s c a l a r should f a l l o f f from k-5/3 near k c = (^/K 3)!/^. The d i s s i p a t i o n i n the pipe was estimated from £ - u 3 /^z to be about 5x 10 3 cm s e c - 3 which agrees with Laufer's (1954) measurements of 4 x 10 3 cm^sec - 3 f o r a higher Re flow. Hence k c f o r the pipe flow w i l l be about 0.2cm-l. For run 300/1 the change i n slope occurred at n = 3 which corresponds to k £ O.lcm -^. This good agreement supports the hypothesis that the f a l l o f f from f 1.0 was due to mixing In the tube and hence not a r e s u l t i n d i c a t i v e of atmospheric humidity f l u c t u a t i o n s . 94 APPENDIX I I I TABULATION OF RESULTS LADNER A l l r e s u l t s i n cm sec , °C, or g/Kg. TABLE AIII.'l tt RUN DATE DURATION u 5 s/L z I\ I 2 1 : ;/I 15 AUG 2 0 5 7 - 2 1 0 9 111 -0 . 0 6 3 0 0 2 2 1 6 / 2 15 AUG 2 1 0 9 - 2 1 2 1 220 - 0 . 0 0 0 0 0 2 1 6 / 3 15 AUG 2 1 2 1 - 2 1 3 2 163 - 0 . 3 8.2 0 0 >, 2 1 8 / 1 16 AUG 1 3 5 3 - 1 4 0 5 480 -0 . 1 7 8 0 0 5 2 1 8 / 2 / 1 15 AUG 14 2 0 - 1 4 3 4 435 - 0 . 1 9 0 0 . 0 2 1 8 / 2 / 2 16 AUG l i i 3 4 - 1 4 4 7 409 - 0 . 1 5 7 0 0 7 2 1 9 / 1 16 AUG 1 5 2 1 - 1 5 3 6 3 94 - 0 . 2 2 0 0 . 0 3 2 1 9 / 2 16 AUG 15 3 6 - 1 5 5 0 335 - 0 . 2 4 0 0 . 0 0 2 1 9 / 3 16 AUG 1 6 6 0 - 1 6 0 5 3 61 - 0 . 2 3 5 0 . 0 10 2 1 9 / 4 16 AUG 1 6 0 5 - 1 6 1 9 361 - 0 . 2 1 2 0 , 0 11 2 2 0 / 1 / 1 21 AUG 1 3 2 1 - 1 3 3 8 334 - 0 . 4 71 -c. 034 12 2 2 0 / 1 / 2 21 AUG 1 3 3 8 - 1 3 5 5 294 - 0 . 5 48 - o . 039 13 2 2 0 / 2 / 1 21 AUG 1 4 1 9 - 1 4 3 4 352 - 0 . 3 08 - o . 017 14 2 2 0 / 2 / 2 21 AUG 1 4 3 4 - 1 4 4 3 403 . - 0 . 18 0 - o . 009 15 2 2 1 / 1 21 AUG 1 5 5 8 - 1 6 1 3 339 - 0 . 6 2 0 - 0 039 16 2 2 1 / 2 21 AUG 1 6 1 3 - 1 6 2 9 307 - 0 . 2 8 5 - 0 0 22 17 2 2 1 / 3 21 AUG 1 6 2 9 - 1 6 3 6 2 45 - 0 . 5 3 7 - o . 049 18 2 2 2 / 1 21 AUG 1 2 3 0 - 1 8 4 7 319 - 0 . 2 6 8 - o . 006 19 2 2 2 / 2 21 AUG 1 8 4 7 - 1 9 0 5 297 - 0 . 2 7 8 - 0 . 007 20 2 2 2 / 4 21 AUG 1 9 0 9 - 1 9 2 7 263 - 0 . 2 9 4 - 0 . 004 21 2 2 3 / 1 21 AUG 2 0 0 4 - 2 0 1 5 155 - 0 . 4 4 8 0 . 006 22 2 2 3 / 2 21 AUG 2 0 1 5 - 2 0 2 6 139 - 0 . 3 0 3 0 010 23 2 1 7 / 1 22 AUG 9 3 3 - 950 445 - 0 . 136 - o . 005 24 2 1 7 / 2 22 AUG 9 5 0 - 1 0 0 7 501 - 0 . 1 3 1 - 0 004 25 2 1 7 / 3 22 AUG 1 0 0 7 - 1 0 2 4 492 - 0 . 1 9 1 - o , 0 04 2 6 2 2 4 / 1 22 AUG 1 2 0 4 - 1 2 1 3 5 26 - 0 . 1 1 0 - o . 004 27 2 2 4 / 2 22 AUG 1 2 1 8 - 1 2 3 1 508 -c . 1 4 6 - 0 . 005 28 2 2 4 / 3 22 AUG 1 2 3 1 - 1 2 4 9 48 7 - 0 . 1 9 8 - o . 008 29 2 2 4 / 4 22 AUG 1 2 4 9 - 1 2 5 4 48 7 - 0 . 1 5 4 - 0 006 30 3 0 0 / 1 22 AUG 143 6 - 1 4 4 9 63 7 - 0 . 0 5 1 - o . 002 31 3 0 0 / 2 2 2 AUG 1 4 4 9 - 1 5 0 2 5 96 - 0 . 0 5 7 - o . 002 32 3 0 0 / 3 ' 22 AUG 1 5 0 2 - 1 5 1 5 506 - 0 . 0 5 7 - o , 002 33 3 0 0 / 4 22 AUG 1 5 1 5 - 1 5 2 3 585 - 0 . 0 6 7 - o . 002 34 3 0 0 / 5 2 2 AUG 15 2 8 - 1 5 4 2 55 7 - 0 . 0 6 8 - o . 003 35 3 0 0/LONG 22 AUG 1 4 3 5 - 1 5 3 0 592 - - 0 . 0 5 7 . - o , 0 9 2 3 6 3 0 1 / 1 22 AUG 1 5 5 4 - 1 6 0 7 55 2 - 0 . 0 6 3 -n, 005 37 3 0 1 / 2 22 AUG 1 6 0 7 - 1 6 2 0 567 - 0 .0-42 - o . 0 03 3 0 3 0 1 / 3 2 2 AUG 1 6 2 0 - 1 6 3 3 5 62 - 0 . 0 4 6 - o . 0 03 39 3 0 1 / 4 2 2 AUG 1 6 3 3 - 1 6 4 6 576 - 0 . 0 45 0 . 0 40 3 0 1 / 5 22 AUG 1 6 5 3 - 1 6 5 9 5 60 - 0 . 0 5 3 0 . 0 41 •302/1 22 AUG 1 7 1 3 - 1 7 2 7 472 - 0 . 0 4 6 - o . 003 '+2 3 0 2 / 2 / 1 22 AUG 1 7 3 5 - 1 7 5 0 509 - 0 . 0 2 6 - o . 0 01 43 3 0 2 / 2 / 2 22 AUG 1 7 5 0 - 1 8 0 2 486 - 0 . 0 3 3 - o . 002 iili 3 0 2 / 3 22 AUG 1 3 0 2 - 1 8 1 6 463 - 0 . 0 2 3 - o . 0 02 45 3 0 3 / 1 / 1 22 AUG 1 9 1 5 - 1 9 2 9 327 0 . 0 3 9 - 0 . 0 03 4 5 3 0 3 / 1 / 2 22 AUG 192 9 - 1 9 4 2 302 0 . 0 83 0 02 h7 3 0 3 / 2 / 1 22 AUG 1 9 5 4 - 2 0 0 5 155 0 . 653 0 . 001 TABLE A l i l . l (CONT.) tt RUN DATE DURATION u z/L 48 3 0 3 / 2 / 2 0 0 AUG 0 p f i r ; _ 2 0 1 6 1 4 3 1 . 5 3 3 n n r\ 7 4 9 30 4/1 22 AUG O p i- ~j _ 2 1 1 0 1 £ A j. ~' 3 . 7 1 ? <\ 0 C 5fi 3 0 4 / 2 2 2 AUG 2 1 2 4- 2 1 3 5 1 9 5 0 . 3 7 6 r> .'.- j-5 1 3 0 5 / 1 / 1 2 2 AUG 2 2 0 8 - 2 2 1 9 n .i n /_ I.''./ r , 0 c, o 0 n n r. 5 2 3 0 5 / 1 / 2 2 2 AUG 2 2 1 9 - o o o <*i ^ L £ C' 2 0 7 L . 10 3 r\ r-.«;..' 0 5 3 3 0 5 / 2 22 AUG 2 2 2 8 - 2 2 4 1 1 9 4 .7 33 ,'\ ;•- ^ ,~\ . J 5 4 3 0 5 / 3 / 1 22 AUG 2 2 4 ? -2 2 5 3 1 3 3 r, Q q c • n . 0 0 1 5 5 3 0 5 / 3 / 2 2 2 AUG 2 2 5 3 - 2 3 0 4 1 0 3 1 . 2 5 3 v.- • J. 'V 5 6 3 0 6 / 1 2 3 AUG 1 0 1 6 - 10 3 0 3 0 9 -0 . 3 8 4 -0 . 0 1 7 5 7 3 0 G / 2 2 3 AUG 1 0 3 4- 1 0 4 9 3 0 3 - p . 3 2 1 -0 . 0 1 2 5 8 3 0 5/3 23 AUG 1 0 5 4 - 1 1 0 3 3 0 6 '.t . 4 9 9 *• 0 . 0 1 6 5 9 3 0 8/4 2 3 A U G 1 1 1 0 - 1 1 2 4 2 9 3 . 3 6 5 ~• p . 0 1 1 5 0 3 9 7 / 1 2 3 AUG 1 2 1 0 — 1 2 2 3 3 63 -0 . 3 5 7 -0 . 0 1 1 6 1 3 0 7 / 2 2 3 AUG 1 2 2 3 - 1 2 3 5 3 2 7 -0 . 3 8 0 -0 . 0 1 4 62 3 0 7 / 3 2 3 AUG 1 2 3 5 - 1 2 4 7 2 9 3 - 0 . 5 6 7 -0 01 P 63 3 0 7 / 4 2 3 AUG 1 2 4 7 - 1 3 0 0 2 7 3 _ n \J .3 64 0 n 61* 3 0 7 / 5 2 3 AUG 1 3 0 0 - 1 3 1 2 2 5 1 _ n . 5 5 4 0 .0 65 307/LONG 23 AUG 1 2 1 0 - 1 2 5 7 3 2 7 -0 . 3 3 3 - 0 . 0 1 1 6 6 3 0 8 / 1 2 3 AUG 1 3 3 4 - 1 3 4 3 3 3 2 u /, O O • * -r / - O -0 . 0 1 4 67 3 0 8 / 2 2 3 AUG 1 3 5 4 - 1 4 0 5 3 9 4 - 0 . 2 4 3 -0 . 0 0 9 6 8 3 0 8 / 3 / 1 2 3 AUG 1 4 0 7 - 1 4 1 8 43 6 -0 . 2 2 1 -0 . 0 0 8 6 9 3 0 8 / 3 / 2 23 AUG 1 4 1 8 - 1 4 2 9 4 4 3 - 0 . 1 9 5 -0 . 0 0 7 70 3 1 8 / 1 / 1 2 3 AUG 1 5 2 4 - 1 5 3 8 3 5 2 -0 . 0 3 3 0 .0 7 1 313/1/2 2 3 AUG 1 5 3 8 - 1 5 5 1 3 2 8 -0 . 1 0 0 0 .0 72 3 1 8 / 2 / 1 2 3 AUG 1 G 2 3 - 1 6 3 7 3 1 2 -0 . 0 8 3 ' o .0 7 3 3 1 3/2/2 2 3 AUG 1 6 3 7 - 1 6 5 0 3 2 4 -0 . 0 9 1 o n 74 3 0 9 / 1 / 1 2 3 AUG 17 4 6- 1 7 5 9 3 5 9 -0 . 1 3 7 - n . 0 0 3 75 3 0 9 / 1 / 2 2 3 AUG 1 7 5 9 - 1 8 1 1 3 4 9 -0 . 1 1 7 -0 . 0 0 7 76 3 0 9 / 2 / 1 2 3 AUG 1 3 1 3 - 1 8 25 3 1 8 -0 . 1 4 2 - 0 . 0 1 2 7 7 3 0 9 / 2 / 2 2 3 AUG 1 8 2 5 - 1 8 3 3 2 9 4 -0 . 0 0 8 - 0 . 0 0 7 78 3 0 9 / 3 2 3 AUG 1 8 4 3 - 1 3 5 4 2 4 1 -0 . 0 7 1 -0 . 0 1 5 7 9 3 1 0 / 1 2 3 AUG 2 0 3 4 - 2 0 4 6 1 6 7 1 . 3 4 9 0 . 1 0 4 30 3 1 0 / 2 2 3 AUG 20 4 9 - 2 1 0 4 2 2 3 0 . 0 0 3 o .0 03 8 1 3 1 0 / 3 2 3 AUG 2 1 1 5 - 2 1 2 6 1 3 0 0 . 4 7 2 0 . 0 1 9 3 2 3 1 1 / 1 / 1 2 4 AUG 1 0 1 1 - 1 0 2 4 6 3 4 -0 . 0 4 9 _ n . 0 0 1 8 3 3 1 1 / 1 / 2 2 4 AUG 10 2 4 - 1 0 3 7 6 1 3 -0 .0 63 .0 0 1 84 3 1 1 / 2 / 1 2 4 AUG 1 0 4 3 - 1 0 5 6 5 3 8 -0 . 1 4 5 - c .0 03 85 3 1 1 / 2 / 2 24 AUG 1 0 5 6 - 1 1 1 0 5 7 8 _ n . 10 9 - 0 n n 3 6 3 1 2 / 1 / 1 2 4 AUG 1 1 3 7 - 1 1 5 1 5 8 4 - 0 . 1 3 1 -0 . 0 0 2 3 7 3 1 2 / 1 / 2 24 AUG 1 1 5 1 - 1 2 0 4 5 6 2 -0 0 o 0 • J I.- L. - 0 . 0 0 2 0 0 1 j Ij 3 1 2 / 1 / 3 2 4 AUG 1 2 0 4 - 1 2 1 3 7 1 1 .0 75 -0 . 0 0 2 8 9 3 1 2 / 2 / 1 2 4 AUG 1 2 1 9 - 1 2 3 0 C 4 3 - 0 . 0 6 1 _ o . 0 0 1 90 3 1 2 / 2 / 2 24 AUG 1 2 3 0 - 1 2 4 2 7 0 0 - n j** o rt • vJ O >> — ^ u . 0 0 1 9 1 3 1 4 / 1 2 4 AUG 1 3 3 6 - 1 3 4 9 4 94 _ n . 1 7 2 _ n . 0 0 2 n o 3 1 4 / 2 2 4 AUG 1 3 4 9 - 1 4 0 3 45 6 -0 . 1 2 1 -0 . 0 0 3 93 3 1 4 / 3 2 4 AUG 1 4 0 3 - 1 4 1 1 4 2 0 _ n . 1 0 5 _ n . 0 0 2 97 TABLE A l l I . I I tt z/L u * q* u ft u * T* 9* 1 -0.07 17.5 2 0.191 0.0 2 . 4 9 2. 0 4 1 .52 3. 32 •.V * * * ft ft ft o -0.00 14.25 0.000 0.0 0 2 . 01 1 .51 4103. 37 * * ft ft * ft 3 -0.38 11.09 0.423 0.0 5 8 2. 5 9 1 q n I ! 59 ft ft ft *5r ft ft ft 4 -0.18 25.46 1.162 0.0 2. 6 9 2 72 1 .36 4 2 ft ft ft ft ft ft ft 5 -0.19 25.30 1.136 0.0 « 6 8 2. 57 1 .74 n 4 2 ft ft ft ft ft ft ft fi -0.16 2 7.20 1.084 0.0 2. 34 n /'. • 2 5 1 .65 n t 4 4 ft ft ft ft ft ft ft 7 -0.22 21.28 0.933 0.0 2. 4 9 2. 7 2 1 . 3 4 o 39 ft ft ft ft ft ft ft r> u -0.24 2 0.00 0.896 0.0 0 61 2. 72 1 . 8 4 n . 35 ft ft ft ft ft ft ft g -0.24 20.00 0.879 0.0 2. 79 2. O 0 1 .80 o. 4 0 ft ft ft ft ft ft ft 10 -0.21 20.17 0.8 08 0.0 7 8 2. 68 1 .79 n. 41 ft ft ft ft ft ft ft 11 -0.47 2 H. • 2 JL 1.838 0.800 2. 59 2. 51 1 .57 o. 46 0.51 12 -0.55 23.02 2.519 1.0 74 0 59 2. 32 1 .54 40 0.45 13 -0.31 27.93 2.121 0.704 n 16 2. 11 1 .37 n 51 0.5 3 14 -0.18 31. 62 1.605 0.448 l'. 98 1. 78 1 .26 f i 61 0.74 15 -0. 62 18.71 1.911 0.7 20 2. 93 2 . 93 1 .82 0 . 42 0.51 16 -0.28 23.24 1.334 ' 0.626 ' 2. 05 2. 41 1 .42 0. 5 4 0.57 17 -0.5 4 17.89 1.467 0.820 75 2. '•J u 1 . 62 f\ 44 0.51 18 -0.27 17.83 0.774 0.103 2. 2 4 2. 09 1 .56 f> U • 52 1.20 19 -0.28 16.5 8 0.6 93 0.10 6 2. 13 1. 88 1 .51 0. 5 3 1.04 20 -0.29 15.00 0.607 0.050 2. 33 0 4* • 01 1 .57 u * 56 1. 78 21 -0.45 9.85 0 . 4 0 9 -0.029 1. 85 1. 62 1 .44 0. 54 0. 6 8 22 -0.30 9.2 2 0.247 -0.043 1. 88 1. 5 4 1 .30 0. 73 0.63 23 -0.14 24.90 0.756 0.15 5 2. 59 2. 2 8 1 .64 0. 67 1.10 2 4 •* 0 » X 3 28.28 0.9 46 G .161 o 35 2 . 3 4 1 .65 0 . 53 0.75 25 -0.19 2 4.49 1.041 0.119 o 85 « 6 0 1 0 0 » /- 0 . 55 1.09 «-i r-L 0 -0.11 3 8.08 1.425 0.32 0 /- . 19 1. 33 1 .36 0. 54 0.59 27 -0.15 32.56 1. 2 9 S 0.260 2. 43 1. 34 1 .40 0. 5 9 0.73 2 8 -0.20 O O n -1 . 1 6 • u .1 1.4 67 0.3 64 n . 53 n /. . 07 1 .5 7 ft 53 0.5 5 2 9 -0.15 31.46 1.35 9 0.317 35 1 . 9 0 1 . 43 0 . 6 0 0.5 7 ^ u — 0 ^ ^ 51.20 1.210 \J • /. J O 2 . 05 1. 7 4 1 . 3 6 n 6 2 0.76 31 -0.06 47.5 4 . 1.183 0.214 2. 15 1. 9 2 1 .35 0. 6 0 0.39 32 -0.06 46.80 1.133 0.234 9 13 1. 79 1 r, 15 J3 0.81 33 -0.0 7 44.50 1.2 08 0.25 6 0 17 n /- • 12 1 . 4 6 0. 73 3 4 -0.07 43.47 1.162 0.2 71 2 . 10 l . 91 1 .41 n 57 0.70 35 _ n n c 47.75 1.178 0.237 "l\ 2 4 i . 9 7 1 .38 n . 0.3 5 3 6 -0.06 4 0.50 0.901 0.425 2. 33 2. 0 6 1 . 51 0. 63 0.49 37 -0.04 47.22 0.826 0.361 0 /- . 14 1. 8 0 1 .29 0. C p ' 0.55 3 8 -0.05 45 . 28 0.8 45 0 . 2 3 3 L . 06 1. 81 1 .36 n. 62 n c c 'j • -> 39 -0.04 43.01 0.779 0.0 2. 12 1. 9 4 1 .42 n 5 6 *.'.- ft ft ft ft ft ft 40 -0.05 40.37 0.811 0.0 2 08 1. 97 1 .53 53 ft ft ft ft ft ft ft 41 -0.05 40.25 0.65 2 0.222 2. 05 1. 73 1 .35 6 7 0.58 4 2 -0.03 4 4.72 0.472 0.135 0 /- . 0 9 1. 67 1 .30 o . 74 0.3 9 4 3 -0.03 35.50 0.366 0.105 o 2 6 1. 97 1 .41 0. 79 1.24 44 -0.02 39.37 0.304 0.184 n £• . 04 1. 73 1 .33 1*1 6 6 0.8 7 45 0.04 25.30 -0.251 0.0 87 2. 26 1. 94 1 .48 0. 30 0. 95 4 6 0. 08 20.74 -0.341 0.051 2. 60 2. 10 1 .60 r- 73 1. 42 47 0. 66 8.49 -0.442 -0.004 n 95 2. 39 1 .85 0 . 75 8.00 98 TABLE A l l I . I I (CONT.) tt z/L u* T* q* S\7 <Jw fir <3q L l * u* u * q* 4 8 1 .53 5.74 -0 . it 8 7 - n . 0 0 4 3 .4 f- .51 9 1 1 0 . 3 , n 4.37 4 5 3 .72 2 . 3 3 f\ \ • • <r- >.-• J _ r\ .035 i P, ^  3 0 p 2. 3 7 1 . 3 6 l . M 5 0 2 o o . o o 3.16 . 2 61 p rt p 4.24 !42 2. 31 0 9 2 1.7 7 51 Q .29 7.21 -0 .13 2 _ n .0 24 / . « 2 . 12 i 5 0; 1 0 n 1 9 rt 5 2 4 . 19 2.37 .211 - 0 .011 3.68 9 . ' 3 7 2. 9 r-i .•1 L rt 1, r-. L,t 0 5 3 5 • / u 2.12 - 0 .2 36 -0 .005 ;• i, ? 3 >~ "7 9 2 6 1 7 00 5 4 1 .00 3 . 3 7 U .13 6 -0 . 0 0.1 3.0 0 . 4 5 1. r 0 I ) 10 5.89 5 5 7 .25 0.73 — 0 .034 — n r\ X • \J \J J 4.53 0 0 0 L. . 51 7. [33 9. 61 i~ C »> 'O -0 .33 22.58 1 .749 f. . 4 0 L 2.3 7 .51 1. 5 9 n . 41 0.48 57 *-\ — i; .32 2 5.69 1 .9 07 n . 4 0 5 2 . Q 9 0 .30 1. 5 0 . 43 1" s 0 5 8 -0 .50 20.74 1 . 9 41 fi .354 o r: T JL • JL 2 .*3 2 1 7 3 p .41 0.51 59 -0 .37 22.14 •1 . 625 n u rt o T , i . o l 2.8 9 2 .47 1 . 5 2 n \ J .49 0.64 6 0 -0 .36 2 4.7 0 1 .93 4 r> .35 6 2.75 .71 1. 73 rs ij 0! 79 51 -0 .33 2 5.45 2 .410 0 .5 20 2.74 /_ .50 1. 67 P .43 62 -0 .57 2 2.58 2 .535 0 .4 69 2.8 8 0 .86 1. 69 0 . 4 0 0.58 63 -0 .36 2 7.02 2 .498 0 .0 2.43 2 .36 1. 4 9 0 .43 A * * A *.# * 64 -0 .55 22.36 o .605 0 . 0 3.09 3 .14 1. 83 0 .40 * * * A * * A 65 -0 .33 24.49 2 .102 o !337 3.09 9 .84 1. 60 .47 0.80 66 -0 .43 24.70 2 .379 0 .459 2.69 3 .11 1. 56 0 .42 0.55 67 -0 .25 28.28 1 .803 0 .332 2.33 2 .15 1. 51 0 .49 0.55 63 -0 .22 28.98 1 .691 n .357 2.40 9 .24 1. 54 0 .50 0.53 69 — n .19 30.50 1 .643 0 .353 2.35 1 .91 1. 41 0 .54 0.68 70 -0 .03 32.56 1 .659 0 .0 2.00 2 .04 1. 25 n .51 * * * * * * * 71 -0 .10 28. 64 1 .554 0 .0 2.18 ^_ .29 1. 35 0 .61 * * * * * * * 72 -0 .08 28. 98 1 .320 0 .0 2.31 2 .01 1. 26 0 .63 ******* 73 -0 .09 28.11 1 .352 0 .0 2.4 0 2 .21 1 . 3 2 0 . 62 * * * * * * * 74 -0 .14 26.46 0 .850 n .308 2.28 2 .01 1. 50 0 .58 0.49 75 -0 .12 2 6.83 0 .745 9 . 258 2.33 1 . 98 1. 46 0 .56 0.50 76 -0 .14 21. u 8 Q .577 0 .299 2.47 2 .33 1. 50 0 .57 0.74 77 -0 .01 19.49 0 .001 n w .147 2.5 6 .28 1. 1--5 5 4 . 58 61. 97 78 -0 .07 14.49 0 .110 0 .167 2.4 8 9 .43 1. 55 0 .45 0. 90 79 1 .35 4.5 8 - 0 w .240 -0 .115 3.19 2 . 18 1. 79 1 . 25 1.33 80 p. .00 14.18 -0 .0 02 -0 .0 26 2.22 1 . 65 1. 33 119 .09 2.68 81 0 .47 5. S 3 _ n v . - .141 - n .033 2.50 2 .21 1. 41 1 .34 l ! 2 3 82 -0 .05 39.24 Q .675 0 rv n o 2. 47 .23 1 . r .«\ 1.,' u . 6 4 1.00 9 X -0 3 7.56 0 . 3 05 n .104 9 9 0 1 .36 1. 4- 0 f) .67 1. 0 2 O I, '-) lr - 0 .14 29. 48 1 . 128 0 .143 ? . 6 G 9 .22 1. 54 0 .57 1.56 O I) o .11 33.32 1 . 103 0 . 14- 9 o . /.,'. n . 15 1. 5 5 0 . 6 0 1.41 -0 .13 33. 62 1 .3 61 n V . 147 2! 34 2 .39 1. 63 fl .59 1.4 9 8 7 -0 . 0 8 41.11 1 r\ f* T~ . i o :> o . 15 2 2.32 .20 1. 45 rt 6 ^  1. 45 38 -0 .08 41.33 1 .213 Q .137 2.3 8 9 . 0 9 1 . 50 r\ . 65 1. 60 3 9 -0 .06 43 .13 1 .0 43 ,9 . 110 2.43 2 .00 1. 53 0 . 0 ii 1.73 90 -0 .08 3 5 . 0 G 0 .957 •J .069 2. 65 2 .31 1. c 0 U J 0 .66 2.7 4 91 — f> .17 30.33 1 .45 9 n w .115 2.49 9 .46 1. u -> 0 .5 6 2.25 9 2 -0 . 12 ^ 8 Q 8 n .93 2 r. u .121 2.30 2 .22 1. 5 4 rt. .54 1.57 93 -0 .10 2 8.11 0 > .756 0 . 0 3 9 2.53 1 .99 1. 5G 0 .57 1.57 TABLE A I I I . I I I # RUN z/L r uw r wT r wq 1 216/1 -0.07 -0.2 6 0 .07 * * v.- * 2 216/2 -0.00 -0.28 0 .00 3 216/3 -0.21 n .14 ft * * ft * 4 218/1 -0.18 -0.20 0 .51 ft * ft * * 5 218/2/1 -0.19 -0.21 0 .54 ft V; ft ft ft 6 218/2/2 -0.16 -0.26 0 .55 ft ft ft ft ft 7 219/1 -0.22 -0.22 n u .5 6 ft * ft ft ft 3 219/2 -0.24 -0.21 nV/ .61 ft ft ft ft ft 9 219/3 -0.24 -0.20 0 .56 ft ft ft * ft 10 219/4 -0.21 -0.20 0 .55 * ft ft ft ft 11. 220/1/1 -0.4 7 -0.25 0 .55 0.50 12 220/1/2 -0.55 -0.25 0 . 65 0.58 13 220/2/1 -0.31 -0.34 0 .57 0.5 0 14 220/2/2 -0.18 -0.40 0 .52 0.43 15 2 21/1 -0.62 -0.19 Q .52 0.43 16 221/2 -0.28 -0.34 0 .52 0.49 17 221/3 -0.54 -0.22 n . 5 6 0.48 18 222/1 -0.27 -0.29 0 .50 0.21 19 2 2 2/2 -0.28 -0.30 0 .50 0.25 20 222/4 -0.29 -0.27 0 .46 0.14 21 223/1 -0.45 -0.33 0 .52 -0.41 22 223/2 -0.30 -0.41 0 .42 -0.49 23 217/1 -0.14 -0.23 0 .36 0.22 24 217/2 -0.13 -0.26 0 .45 0.33 25 217/3 -0.19 -0.19 0 ikO 0.20 25 22 4/1 -0.11 -0.34 0 .55 0.5 0 27 224/2 -0.15 -0.29 0 .48 0.39 23 224/3 -0.20 -0.2 7 0 .48 0.46 29 224/4 -0.15 -0.30 0 .47 0.4 9 30 3 0 0/1 -0.05 -0.36 0 .43 0.3 9 31 300/2 -0.35 0 .49 0.3 3 32 300/3 - n r< P 1/ • I J U -0.34 A . 4 6 0.35 33 300/4 -0.07 -0.32 0 .45 0.35 3k 3 0 0/5 -0.07 -0.34 o .50 0.41 35 3 00/LONG -0.06 -0.32 0 . 44 0.34 3 6 301/1 -0.06 n. \) . 4 2 n c >, w . -> 4 37 301/2 -0.04 -C.36 0 .46 W . D C : 3 8 301/3 -0.36 Q . 4 8 " r- *7 39 301/4 -0.04 -0.33 r\ i j .50 ft ft ft ft ft 40 301/5 -0.05 -0.31 0 . 4 9 ft ft ft ft ft 41 3 0 2/1 -0.05 -0.36 0 . 4 4 0.51 4 2 302/2/1 -0.03 -0.37 n .41 0.34 43 3 0 2/2/2 -0.03 -0.31 0 .36 0.23 44 302/3 -0.02 -0.37 o . 4 6 0.3 5 45 303/1/1 0.0 4 -0.30 -0 .34 4 5 303/1/2 0.03 -0.24 -0 . 3 4 0.18 47 303/2/1 0.66 -0.18 - 0 .29 -0.03 100 TABLE A I I I . I I I (CONT.) tt RUN 43 3 0 3 / 2 / 2 49 3 0 4 / 1 50 3 0 4 / 2 51 3 0 5 / 1 / 1 52 3 0 5 / 1 / 2 53 3 0 5 / 2 54 3 0 5 / 3 / 1 55 3 0 5 / 3 / 2 56 3 0 6 / 1 5 7 30 6 / 2 58 3 0 6 / 3 59 3 0 6 / 4 60 3 0 7 / 1 51 3 0 7 / 2 62 3 0 7 / 3 63 3 0 7 / 4 64 3 0 7 / 5 65 3 0 7 / L O N G 66 3 0 8 / 1 67 3 0 3 / 2 68 3 0 8 / 3 / 1 69 3 0 8 / 3 / 2 70 3 1 8 / 1 / 1 . 71 3 1 8 / 1 / 2 72 3 1 8 / 2 / 1 73 3 1 3 / 2 / 2 74 3 0 9 / 1 / 1 75 30 9 / 1 / 2 76 3 0 9 / 2 / 1 77 3 0 9 / 2 / 2 78 3 0 9 / 3 79 3 1 0 / 1 80 3 1 0 / 2 81 3 1 0 / 3 32 3 1 1 / 1 / 1 83 3 1 1 / 1 / 2 84 3 1 1 / 2 / 1 85 3 1 1 / 2 / 2 85 3 1 2 / 1 / 1 37 3 1 2 / 1 / 2 88 3 1 2 / 1 / 3 39 3 1 2 / 2 / 1 90 3 1 2 / 2 / 2 91 3 1 4 / 1 92 3 1 4 / 2 93 3 1 4 / 3 z/L r uw 1 . 5 3 - 0 . 1 4 3 . 7 2 - 0 . 1 4 0 Ct o - 0 . 1 0 0 . 2 9 - 0 . 2 6 4 . 1 9 - 0 . 1 2 5 . 7 8 - 0 . 1 0 1 . 0 0 - 0 . 2 1 7 . 2 5 - 0 . 0 8 - 0 . 3 3 - 0 . 2 5 - 0 . 3 2 - 0 . 3 2 - 0 . 5 0 - 0 . 2 2 - 0 . 3 7 - Q . 2 3 - 0 . 3 5 - 0 . 2 1 - 0 . 3 3 - 0 . 2 2 - 0 . 5 7 - 0 . 2 1 - 0 . 3 6 - 0 . 2 7 - 0 . 5 5 - 0 . 1 8 - 0 . 3 8 - 0 . 2 0 - 0 . 4 3 - 0 . 2 2 - 0 . 2 5 - 0 . 2 8 - 0 . 2 2 - 0 . 2 7 - 0 . 1 9 - 0 . 3 0 - 0 . 0 3 - 0 . 4 0 - 0 . 1 0 - 0 . 3 4 - 0 . 0 8 - 0 . 3 4 - 0 . 0 9 - 0 . 3 2 - 0 . 1 4 - 0 . 2 9 - 0 . 1 2 - 0 . 2 9 - 0 . 1 4 - 0 . 2 7 - 0 . 0 1 - 0 . 2 6 - 0 . 0 7 - 0 . 2 5 1 . 3 5 - 0 . 1 8 -J • \i u - 0 . 3 3 0 . 4 7 - 0 . 2 8 - 0 . 0 5 - 0 . 2 5 - 0 . 0 6 - 0 . 3 1 - 0 . 1 4 - 0 . 2 3 - 0 . 1 1 - 0 . 2 6 - 0 . 1 3 - 0 . 2 6 - 0 . 0 3 - 0 . 3 0 - 0 . 0 3 - 0 . 2 8 - 0 . 0 6 - 0 . 2 7 - 0 . 0 3 - 0 . 2 2 - 0 . 1 7 - 0 . 2 4 - 0 . 1 2 - 0 . 2 8 - 0 . 1 0 - 0 . 2 6 r v wT wq - 0 . 2 4 - 0 . 0 4-- 0 . 1 2 - 0 . 1 2 - 0 . 1 9 - 0 . 1 0 _ n u . 1 3 - 0 . 2 0 - n . 1 3 - 0 . 0 7 -6 . 1 7 - 0 . 0 3 - 0 . 2 6 - 0 . 0 0 - 0 . 0 7 - 0 . 0 2 0 . 6 1 0 . 5 3 n . 6 2 0 . 4 5 0 . 54 0 . 4 4 n . 54 0 . 4 1 n . 50 0 . 2 9 n •j . 55 0 . 4 1 0 . 5 9 0 . 4 1 n u . 5 6 - -t- t^* 0 . 54 * ~k * * * 0 . 54 0 . 3 1 n . 5 7 0 . 4 4 n . 54 0 . 4 8 n . 5 2 0 . 4 9 0 . 5 2 0 . 4 2 52 vV * * * 6 . 4 3 * * * * * \j . 5 1 * * * * * 0 4 9 * * * ft 0 . 4 6 0 . 5 5 0 ,43 Q . 5 4 0 . 46 0 . 3 6 0 01 0 . 0 0 0 57 0 . 2 9 - 0 18 - 0 . 1 2 00 - 0 . 1 1 — o u , 21 - 0 . 2 3 39 0 . 2 5 n 43 0 . 2 3 n 4 3 0 . 1 6 43 0 . 1 3 o . 4 2 0 . 1 6 o . 4 5 0 . 1 9 p , 4 0 0 . 1 7 n , 3 3 0 . 1 5 0 . 35 0 . 0 9 n 4 4 0 . 1 1 0 . 48 0 . 1 6 0 4 7 0 . 1 7 101 APPENDIX IV TABULATION OF RESULTS BOMEX A l l r e s u l t s i n cm sec \ °C, or g/Kg. TABLE AIV.I # RUN DATE DURATION u z/L z/q 1 B14/1 6 MAY 1145-1226 670 -0.080 -0.046 2 B14/2 6 MAY 1431-1523 620 -0.067 -0.036 3 B15/1 6 MAY 1811-1854 580 -0.140 -0 .080 4 B15/2 6 MAY 1902-1937 530 -0.129 -0 .068 5 B15/3 6 MAY 1959-2043 370 -0.360 -0 .140 TABLE AIV.II # z/L u* T 1 q*1 ^ Gr u * u * u * T~ q* 1 -0.08 27.8 0.70 0.89 2.0 2.0 1.20 1.0 0.8 2 -0.07 25.9 0.62 0.91 2.0 1.9 1.15 1.1 0.8 3 -0.14 21.7 0.88 0,50 1.9 2.0 1.15 0 .8 0.5 4 -0.13 20.8 0.86 0.50 2.0 1.6 1.10 0.7 0.4 5 -0.36 15.6 0.69 0.42 2.1 1.8 1.44 0.8 0.5 1 - uncalibrated 102 TABLE AIV,11 # RUN z/L 1 B14/1 -0.08 2 B14/2 -0.07 3 B15/1 -0.14 4 B15/2 -0.13 5 B15/3 -0.36 r uw wT r wq -0.40 0.26 0.34 -0.43 0.31 0.45 -0.46 0 .32 0.55 -0.41 0.41 0.65 -0.34 0 .33 0.53 103 APPENDIX V SPECTRUM ANALYSIS RESULTS In t h i s appendix the composite cospectra and s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s o f momentum, heat, and moisture t r a n s f e r f o r s t a b i l i t y Groups II, V, VI, VIIIA, and VIIIB are presented. On each f i g u r e up to seven data runs are presented and the symbols can be i d e n t i f i e d with runs by use o f Table AV.I. A l l cospectra are normalized and p l o t t e d on double logarithmic coordinates TABLE AV.I I d e n t i f i c a t i o n of Runs on Composite Plots See Table AIII.I to i d e n t i f y run numbers. S t a b i l i t y Group • X 4- o A • V I 11 12 15 17 58 62 64 I I I 13 16 19 25 57 68 69 V 30 32 34 37 39 41 88 VI 42 43 44 45 46 77 80 VIIIA 48 49 50 79 VIIIB 52 53 55 104 I .1 .001 .01 10 1-1 c .1 .01-.00H 105 G p VI o ft * *+ W x "!O5I .01 .1 • 10 1-. 5 -o-i c 13 .01-.001A G p VIIIA > + - f 0^01 .01 106 .001 10 107 108 In c .1-7 • 7 • • 7 .01-h .001 G p VIIIA 10 .061 B i J 1-1 5 j J + 0 .01H .ooH G p VIIIB .001 ioi" .1 10 1 4 1 > 1 H .01H -A X 0 X X o •I"* O X ' Gp O o .001-.001 .CJ1 .1 10 .0OH xx5i !oi 3 " i ib 110 . O O H . 001 Zl i r .1 ! 10 I l l to-. .8A .6H .4^ .2-0--.2H -.4-X 0 A • V o G p + A A A 0 + o .001 ,01 y 4. f-A J » , + x A A AjvWJff'A x * 8 +o*f> • • 9 .1 * A _ * A A 10 1.0-. 8H f) .6-4-.2-0--2--4-a t + • 7 + * * A A • o ° • V X ° 7 a n V G p V . X ° o o t> a a ? o + -V-X — .001 — r * .01 .1 i 10 112 1.0-.8-•Ruw ( f^ .6-.4-.2-0--.2--.4-X x " O 6 G p VI X O X v a X a **< o » DV. % q i 6 j -.001 .01 .1 10 10-7 .8-.6-G p VIIIA .4-.2-0--.2--4-T6-o + o . »+X - p B 1 1 10 | f .001 .01 .1 + X X O - 1 10 113 1.0n .8-.6-G p VIIIB .4-.2-0--2--.4-• + + * . 4 . ' x«+ + x -.6- ft x H » x X| * .001 .01 —t 10 1.0-.8H R w T ( f > .6-.4-.2-0--.2-] -4-+ A G p D 0 o o a • .001 .01 .1 To 114 10-i .8-.6-.4-.2-0--.2--.4-A y t Q X •I- o • , * G p V a A .Ho A a + X 6. -* »j .001 .01 T .1 Q o 7o 1.0n + x A 4 .8-.6-.4-.2-0--.2-G p VI # * A + + + x ^ A * + . ^ o t . A 3 j f -.4-.001 x$7 ~r .1 10 115 -*wT ( f ) 1.0-1 .8-f) .6-.4-.2-0 -.2--.4-. -6 G p VIIIA X X X x .001 .01 1^  .1 y » X> * . x x •x . x * I 10 R w T ( f ) 1.0-.8-f) .6-.4-.2-0--.2--.4--.6-X X ° Gp VIIIB ©v • * ^» . V • • o * + • _fi 12 !X + + • o o + X X X + 001 01 -i r 1 t 1 10 116 1.CH .8H R (f ) W C | .6 .4-.2-0--.2-• n • x A y G p 0 + • n V & a *fc o A <; * 0 9 A 0 + « » °XVX o •a -4- y 8i A .001 .01 .1 10 1.0-1 .4-.2-0--.2-Q + X A O .X A Q U ' G p V A »o OS + ' A * o A A x <s A A* oo A + -.4- -B A)i A |A&eB .001 .01 .1 ~1 10 117 1.0-. JBr\ .6-.4-.2-0-G p VI o o ?• 4-A * C ° ° K _ M — 0 -2^-1 -.4-4 A o .001 .01 .1 10 L i s t of Symbols 118 0 ^ s p e c i f i c heat of a i r at constant pressure. D molecular d i f f u s i v i t y o f water vapour, q Drj, molecular condu c t i v i t y f o r heat. 6r. = 1 f o r i , j . k , c y c l i c ; = -1 f o r i , j , k not c y c l i c ; = 0 f o r any of 1 J K i , j , k equal, f n a t u r a l frequency, = nz/u. i th component o f earth's g r a v i t y . ^L_.(n) c o s p e c t r a l energy density between i and j at frequency n (eqn. 2.3) K turbulent d i f f u s i v i t y (eqn. 2.8). <^ von Karman's constant,= 0.4. L Monin-Obukhov length (eqn. 2.6). n frequency, i n Hz. P atmospheric pressure, q s p e c i f i c humidity. q 4 s c a l i n g parameter f o r humidity (eqn. 2.7c). R _ ( f ) s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t f unction (eqn. 2.5). r . . c o r r e l a t i o n c o e f f i c i e n t (eqn. 2.7). p density o f a i r . rr- standard deviation o f x. -y x T temperature. T v v i r t u a l temperature. s c a l i n g parameter f o r temperature (eqn. 2.7b). u^ v e l o c i t y component i n the x^ d i r e c t i o n , u mean wind speed. u A f r i c t i o n v e l o c i t y (eqn. 2.7a). _ 0 - . j th component of the earth's r o t a t i o n vector. 0 molecular v i s c o s i t y , 

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