DUDIEY KNOX LIBRARY NAVAL i-OSTGRAUL' ME SCHOOL MONTEREY, CALIFORNIA 93940 UNIVERSITY OF CALIFORNIA San Diego Comparison of Momentum, Sensible and Latent Heat Fluxes Over the Open Ocean Determined by the Direct Covariance, Inertial and Direct Dissipation Techniques A dissei'tation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Oceanography by Gregory Frank Dreyer Committee in charge: Professor Carl H. Gibson, Chairman Professor Robert S. Arthur Professor Paul A. Libby Professor Fred N. Spiess Professor SiebertQ. Duntley Doctor Carl A. Friehe 1974 T161533 The V7 NAVAL f-OSTGRADL'ATE SCHOOL MONTEREY, CALIFORNIA 93940 The dissertation of Gregory Frank Dreyer is approved-r^and it is acceptable in quality and lorrryiop publication on^riicrofilm: DEDICATION To Karolyn, Racheal and Gwen, who . . . "really know what this means, " 111 TABLE OF CONTENTS Page List of Symbols - List of Figures • List of Tables Acknowledgment Vita, Publications and Fields of Study Abstract . Introduction Flux Techniques ■ 2. 1 Direct Covariance Technique 2.2 Dissipation Technique 2.2a Inertial-di ssipation technique 2.2b Direct-dissipation technique 2. 3 Stability Considerations 2.4 Budget Equations ■ . . Instrumentation and Data Analysis 3. 1 Experimental Arrangement 3. 2 Data Acquisition 3. 2a Temperature measurements 3. 2b Humidity measurements 3.2c Velocity measurements 3. 2d Analog instrumentation 3. 3 Data Processing 3. 4 Velocity Pitch Corrections Results 4.1 Times Series Analysis 4. 2 Standard Deviations of Turbulent Fluctuations and their Stability Dependence 4. 3 Pitch Corrected Covarianccs and Error Analysis 4. 4 Flux and Correlation Results 4. 5 Spectra 4. 5a Velocity spectra 4. 5b Temperature and humidity spectra . . VI xiii xx xxi xxii xxiv 1 4 4 7 9 11 12 15 24 24 31 34 35 39 41 42 54 • 58 58 82 90 98 103 105 137 IV J ater Page 4. 6 Cospectra 162 4. 6a Cospectra of momentum (^w) 163 4. 6b Cospectra of heat and water vapor flux (w9, wq) 172 w6 cospectra 172 wq cospectra 4.6c Cospectra of hori2;ontal heat and vapor flux (u 9 , uq) 199 4. 6d Cospectra of temperature and humidity (6q) . . . .219 4. 7 k Spectra and Comparison of Flux Techniques . . 232 4. 7a Comparison of eddy correlation and inertial dissipation techniques 233 Momentum flux 233 Heat and water vapor flux • . . . 242 4. 7b Comparison of eddy correlation and direct dissipation techniques 251 4. 7c Scalar variance budgets reeamined ...... 267 4. 8 ' Application of the Bulk Aerodynamic Technique for Estimation of the Turbulent Heat Fluxes ..... 278 5. Summary and Conclusions . 282 5. 1 Momentum Flux 282 5.2 Latent Heat Flux 286 5. 3 Sensible Heat Flux 289 5. 4 Model of the Atmospheric Surface Layer Over the Ocean 295 5. 5 Recommendations for Further Studies 301 References 304 Appendix 1 312 LIST OF SYMBOLS Second order horizontal velocity structure function subrange constant, dimensionless Rate of work done by turbulence on buoyancy forces, cm /sec Second order scalar structure function subrange constant, dimensionless Turbulent drag coefficient, dimensionless Specific heat, cal/gm - °C Constant in the stability expression for a /q0, , dimensionless Constant in the stability expression for a /T , , 0 * dimensionless Constant in the stability expression for 0" /u , , w :': a imens ionle ss Non-dimensional flux divergence of turbulent kinetic energy transport Non-dimensional flux divergence of pressure transport Second order horizontal velocity structure 2 / 2 function, cm /sec 2 Scalar molecular diffusivity, cm /sec 2 Second order scalar structure function, C , 3 2 (figm/cm ) 10 log (Power (l)/Power (2)), dimensionless vi 2 2 e Kinetic energy per unit mass, cm /sec e.. = — (u. .+ u. .) Symmetric rate of strain tensor, sec f Frequency, Hz f Normalized frequency, f z/U , dimensionless G(z/L) Stability function for normalized -cospectrum, dimensionless UWfN g Acceleration of gravity, 978 cm/sec j k,b,6 j.j . -1 grad - — + - — + - — , gradient operator, cm 6 x o y 5 z H Turbulent latent heat flux, mw/cm 2 H Turbulent sensible heat flux, mw/cm H (z/L) Stability function for normalized u9L u * j- • i N -cospectrum, dimensionless H (z/L) Stability function for normalized w 8 f w 7. . • N -cospectrum, dimensionless H^ (z/L) Stability function for normalized 0q f 9q ' . N -cospectrum, dimensionless I Pressure transport required to balance the 2 . 3 kinetic energy buaget, cm /sec K von Karman's constant, 0.4 , dimensionless K Turbulent eddy transfer coefficient for water vapor, dimensionless K Turbulent eddy transfer coefficient for sensible heat, dimensionless K , Turbulent eddy transfer coefficient for M " . . momentum, dimensionless vi 1 ~4 ~2 - ■ K(x) • Kurtosis of the variable x , x /(x ) , x = 0 , dimensionless k Radian wavenumber, 2nf/U , cm L Monin-Obukhov length, u , T /Kg w9 , * v v dimensionle s s L Energy scale, production scale, cm o L Latent heat of vaporization, cal/gm t Instrument sensing path length, cm M Mean specific humidity, gm/gm M (z/L) Stability function for normalized uq f -cospectrum, dimensionless m Fluctuating specific humidity, gm/gm p Pressure,, mb 3 q Absolute humidity, jugm/cm R Radiation interaction with temperature field, °C/sec R Bowen ratio, dimen&ionless B / 1/2 R (f) Spectral correlation coefficient, <3? /(<& * ) , uw .. . \xw uu WW dimensionless r Separation distance, cm r Correlation coefficient, xy/cr (J , dimensionless xy x y S General source term of the humidity variance 3 2 budget equation, (jLtgm/cm ) /sec General source term of the t-irnperature variance 2 budget equation, °C /sec Vlll ~3 7 3/2 _ Skewness of the variable x , x /(x ) , x = 0 , dimensionless Rate of evaporation, /Ltgm/cm - sec Temperature, ° C Virtual temperature (includes humidity effects), °C Time, seconds Horizontal velocity, cm/sec Fluctuating horizontal velocity, cm/sec Velocity component in the ith direction, ' cm/sec Output voltage, volts Fluctuating transverse velocity, cm/sec Fluctuating output voltage, volts. Vertical velocity, cm/sec Fluctuating vertical velocity, cm/sec Horizontal coordinate, cm Spatial coordinate in the ith direction, cm Transverse coordinate, cm Vertical coordinate, height above the mean sea surface, cm Inertial subrange constant for velocity (k-spectrum), dimensionless Inertial subrange constant for xy covariance (f - cospectrurn), dimensionless N ^ IX H Ratio of turbulent eddy transfer coefficients, dimensionless Inertial subrange constant for humidity (k - spectrum), dimens ionle s s Inertia! subrange constant for temperature (k-spectrum), dimensionless Scalar, temperature or humidity, °C and /Llgm/cm Differential operator Rate of viscous dissipation of turbulent kinetic 2 3 energy per unit mass, cm /sec 3 1/4 Dissipation scale, (v /c) , cm Mean potential temperature, ° C Fluctuating temperature, ° C Constant in Lyman-alpha humidiometer output equation, (jugm/cm ) 2 Molecular kinematic viscosity, cm /sec 3. 14159* • • > dimensionless 3 Density", gm/cm Constant in the stability expression for the dimensionless scalar gradient, dimensionless Constant in the stability expression for the dimensionless wind shear, dimensionless Standard deviation of the variable x , (units of x) Turbulent shear stress, dynes/ cm Turbulent shear stress at the ocean surface, dynes / cm x $ Dimensionless humidity gradient B $ Dimensicmless temperature gradient H $ Dimensicmless wind shear M (f or k) Spectrum of x , units of x per Hz or cm xx $ (f) Cospectrum of xy covariance, units of x . v per Hz 4? Dimensicmless viscous dissipation of kinetic energy

(as suming total production = Cl dissipation of kinetic energy) plotted versus normalized frequency . 127 22 Average vertical velocity spectra normalized 2 2/3 with u, and ' (Wyngaard and Cote ) expression for normalized dissipation plotted versus normalized frequency 131 24 Average vertical velocity spectra normalized 2 2/3 with u. and $ plotted versus normalized C2 frequency 133 25 Spectral ratio <£> /<£ plotted versus ww uu normalized frequency 136 26 SOMA temperature spectra plotted versus frequency 139 27 MITOS I temperature spectra plotted versus frequency 141 28 MITOS III and OWAX temperature spectra plotted versus frequency 143 29 SOMA humidity spectra plotted versus frequency. . 145 30 MITOS I humidity spectra plotted versus frequency 147 xv Figure ■ Page 31 MITOS III and OWAX humidity spectra plotted versus frequency ......... 149 32 Average temperature spectra normalized with 2 T plotted versus normalized freq\iency . .... 152 2 33 Average humidity spectra normalized with q , plotted versus normalized frequency ....... 154 34 Average temperature spectra normalized with 2 T, , <& (dimensionless temperature gradient) *-]/3 and plotted versus normalized frequency (comparison with other results) . . . 157 2 35 Average humidity spectra normalized with q , , $ (dimensionless humidity gradient) and -1/3 $ plotted versus normalized frequency (comparison with other results) 159 36 MITOS III and OWAX momentum flux (uw) cospectra (corrected for pitch) plotted versus frequency . ., 165 2 37 Average uw cospectra normalized with uA plotted versus normalized frequency (comparison with other results) 167 2 38 Average uw cospectra normalized with u^ plotted linearly versus normalized frequency (comparison with other results) „ 170 39 SOMA heat flux (wG) cospectra plotted versus frequency 174 40 MITOS I wQ cospectra plotted versus frequency 176 41 MITOS III and OWAX w9 cospectra plotted versus frequency corrected for pitch 178 xvi Figure Page 42 Average w0 cospcctra normalized with u, T , plotted versus normalized frequency (comparison with other results) 181 43 Average W0 cospectra normalized with u T plotted linearly versus normalized frequency (comparison with other results) 183 44 SOMA water vapor flux (wq) cospectra plotted versus frequency 187 45 MITOS I wq cospectra plotted versus frequency 189 46 MITOS HI and OWAX wq cospectra plotted versus frequency (corrected for pitch) 191 47 Average wq cospectra normalized with u_,,q^ plotted versus normalized frequency (comparison with other results) 194 48 Average wq cospectra normalized with u,q , plotted linearly versus normalized frequency (comparison with other results) 19o 49 MITOS I horizontal heat flux (u0) cospectra plotted versus frequency 201 50 ., MITOS III and OWAX u0 cospectra plotted versus frequency 202 51 MITOS I horizontal water vapor flux (uq) cospectra plotted versus frequency . 205 52 MITOS HI and OWAX uq cospectra plotted versus frequency 207 53 Average uQ cospectra normalized with u,,,T , plotted versus normalized frequency (comparison with other results) 210 54 Average uq cospectra normalized with u (Kz) plotted u * C2 versus radian wavenumber (ordinate represents agreement between direct covariance and inertial dissipation estimates of u_f) 2 36 5/3 63 k average horizontal velocity spectra 2 -2/3 normalized with a u , (Kz) plotted U * €z versus radian wavenumber (ordinate represents agreement between direct covariance and inertial dissipation estimates of u£) 238 5/3 ' 64 k average temperature spectra normalized 2 -1/3 -2/3 with 2T, <£><£> (Kz) plotted versus * H € radian wavenumber (ordinate represents fi„ required for agreement between direct covariance and inertial dissipation estimates of Tjf) 246 xvm Page 5/3 k average humidity spectra normalized with 2 -1/3 -2/3 q, <& $ (Kz) plotted versus radian * E € wave number (ordinate represents 8 required q for agreement between direct covariance and 2 inertial dissipation estimates of q_J 248 -1/3 66 MITOS I runs 1 and 7 k velocity derivative 2/3 spectra normalized with C plotted linearly versus normalized wavenumber (7)k) (ordinate represents a from direct dissipation estimate) u (from McConnell, 1974) 256 -1/3 67 MITOS I runs 1 and 7 k temperature -1/3 derivative spectra normalized with v C plotted linearly versus normalized wavenumber (77k) (ordinate represents B from direct 9 50 . dissipation estimate) (from McConnell, 1974) 258 ture 2/3 -1/3 68 OWAX-4 k velocity and temperature derivative spectra normalized with € -1/3 (velocity) and X Q e (temperature) plotted linearly versus normalized wavenumber (7)k) (ordinate represents (X or B from direct U 9 50 dissipation estimate) (from McConnell, 1974) . . 260 69 Ramp model for temperature and humidity over the ocean 274 xrx LIST OF TABLES Page Environmental Conditions 59 Flux and Correlation 60 Stability Results 83 Pitch Angles and Corrected Fluxes 95 Normalized Correlation Coefficients 102 Spectral and Cospectral Information 104 Cospectral Subrange Constants ■ 231 Direct Dissipation Results 2 53 Comparison of Eddy Correlation and Direct Dissipation Techniques 263 Production and Dissipation of Temperature Variance 268 Bulk Aerodynamic Results 2 80 xx ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to Professor Carl H. Gibson for giving direction and ptirpose to this research. I am most grateful to Drs. Carl A. Friehe and Frank H. Champagne for their encouragement and assistance. A word of thanks is extended to Tom Deaton, Gene Dia.l and Jerome Dayton for their electronic and computer wizardry. I wish to thank my friends and associates at U. C. S. D. , and my colleague, Steve Mc.Connell, for their cooperation and assistance. The author is indebted to Capt. Rich Silva and the crew of FLIP for their invariable assistance during the research cruises. s A special word of thanks for the professional and heroic accomplishment of Jeri Neuberger, who spent many long and extra hours typing and reviewing the dissertation. To Evelyn Portillo for her work on the figures, I am most grateful. Finally, I wish to express my deepest appreciation to my special friends, wife and family for their help and support during this research. The author was supported by The Naval Post-graduate School, Monterey, under The Junior Line Officer Advanced Educational Program (BURKE Program), Contract N 663 14-70-A-0058. xxi VITA October 25, 1945 - Born - Annapolis, Maryland 1963 - 1967 B.S., Mechanical Engineering, U.S. Naval Academy, Annapolis, Maryland 1967 - Officer, U.S. Navy, Qualified in Submarines 1969 - 1974 Ph.D., Oceanography, Scripps Institution of Oceanography, University of California, San Diego PUBLICATIONS Friehe, C. A. , Gibson, C. H. and G. F. Dreyer, "Effects of Temper- ature and Humidity on Density and Refractive Index Fluctuations Over the Open Ocean, " Opt. Soc. Airier. Bull., paper WD- I 5, p. 13, October, 1972. s Dreyer, G. F. , Gibson, C. If. and C. A. Friehe, "Measurements of Temperature and Humidity Fluctuations Over the Open Ocean, " Bull. APS, 17, pp. 1102-1103, November, 1972. Dreyer, G. F. and C. H. Gibson, "The Inertial Subrange of Turbulence Over the Open Ocean," Bull. APS, 16, p. 1306, November, 1971. FIELDS OF STUDY Physical Oceanography Professors Robert S. Arthur, Charles S. Cox, Carl Eckart, Myrl C. Hendershott and Joseph L. Reid Biological Oceanography Professors John A. McGowan, Michael M. Mullin and Richard H. Rosenblatt . Marine Chemistry and Nuclear Geochemistry Professors Harmon Craig and Joris M. T. M. Gieskes Marine Corrosion Mr. Frank LaQue xx 11 Marine Geology Professors Joseph R. Curray, Douglas L. Jnman and Henry W. Menard Mathematics Professors Edward W. Fager and Frank B. Theiss Meteorology Professors Daniel B. Olfe and Stanford S. Penner Fluid Mechanics Professors Carl H. Gibson, Paul A. Libby and Charles Van Atta Radiative Transfer in the Sea Professor Siebert Q. Duntley FIELD OF RESEARCH Micrometeorology Professor Carl H. Gibson xxm ABSTRACT OF THE DISSERTATION Comparison of Momentum, Sensible and Latent Heat Fluxes Over the Open Ocean Determined by the Direct Covariance, Inertial and Direct Dissipation Techniqu by Gregory Frank Dreyer Doctor of Philosophy in Oceanography • University of California, San Diego, 1974 Professor Carl H. Gibson, Chairman Measurements of velocity, temperature and humidity were made in the atmospheric surface layer over the open ocean from the Research Platform FLIP, to compare estimates of the fluxes of momentum, sensible and latent heat, using the direct covariance, inertial and direct dissipation techniques. Measurements were made during a series of oceanographic cruises approximately 60 miles off the coast of Baja California, between August 1970 and April 1973. Direct covariance estimates of the fluxes were corrected for instrument tilt using simultaneous measurements of pitch angle, and dissipation estimates were corrected for stability effects. Agreement was obtained between estimates of momentum xxiv flux by the dissipation techniques and the direct measurements within the uncertainties of the direct estimates (± 25%) , applying the assumption that total production of kinetic energy (mechanical + buoyant) equals dissipation. From, the direct dissipation technique, the average value determined for the velocity subrange constant was a = 0. 53 ± 0. 03 . Trends in the direct dissipation estimates indicate that vertical turbulent transport and pressure transport of kinetic energy cannot be neglected and may be approximately half of the estimates of dimensionless transport measured over land. Comparisons were made between directly measured momentum fluxes corrected for instrument tilt using measured pitch angles, and values obtained using estimates of pitch angle in lieu of measurement. Results of the comparison suggest that large errors in direct momentum flux estimates can be incurred if tilt corrections are based on estimates of pitch angle. For agreement between inertial dissipation estimates and directly measured latent heat fluxes, an average value of the humidity subrange constant B = 0.21 ± 0.05 was required. The direct q dissipation technique was not applied to estimate latent heat fluxes since the frequency response of the Lyman-alpha humidiometer was not sufficient for direct estimates of the dissipation of humidity variance. Dimensional humidity spectra were similar to horizontal velocity pectra, and water vapor flux cospectra were similar to momentum xxv Nflux cospectra. To- obtain agreement between direct estimates of sensible heat flux and inertial dissipation estimates, an average value of the temperature subrange constant 8 = 2. 2 ± 0. 3 was required. 6 Estimates of sensible heat flux by the direct dissipation technique were higher than direct measurements by a factor of 2 or more. From direct estimates of the dissipation of temperature variance (± 20%) and sensible heat flux (± 10%) , dis sipation was greater than production of temperature variance by as much as a factor of 4 , not accounted for by uncertainties in the direct estimates, or by temperature flux divergence. Direct dissipation estimates of 8 varied from 0. 7 ± 6 0. 07 to "2. 4 ± 0. 2 . Temperature spectra from different cruises with different environmental conditions did not compare with one another, and were not similar to humidity or velocity spectra. Cospectra of sensible heat flux exhibited similar differences. The differences between production and dissipation of temperature variance, and the behavior of the temperature spectra and sensible heat flux cospectra could be accounted for by consideration of sources of production ustially neglected in the temperature variance budget, and attributed to the combined effects of ocean spray evaporation and radiative heating/ cooling. A wide range of bulk coefficients were obtained from comparison of estimates of sensible heat flux by the direct covariance and bulk xxvi aerodynamic techniques, indicating the bulk technique is not reliable for estimates of sensible heat fluxes. A value of (1. 29 ± 0. 36) x 10 was obtained for the latent heat flux bulk coefficient. XXVI 1 1. INTRODUCTION Energy and moisture transfer from the oceans to the marine atmosphere are major driving factors of atmospheric and oceanic circulation. Within the last decade a vast amount of scientific investigation and experimentation has been directed toward an understanding of the energy exchanges and physical processes which occur at the atmosphere - ocean interface. Accurate determination of the vertical fluxes of momentum, sensible and latent heat is of prime importance. This research has as its primary objectives the direct s measurement of the turbulent fluxes and comparison of various techniques of estimating the fluxes indirectly from related statistical quantities. Perhaps one of the earliest attempts to estimate the transfer of momentum and heat from, the ocean was made by G. I. Taylor in 1913 from a whaling ship using balloon and kite observations of mean 1 temperatures and wind velocities (Taylor, 1970). Due to severe instrument limitations, early methods of estimating the turbulent fluxes have consisted of semi-empirical theories relating mean properties or gradients to the actual fluxes. No direct flux calculation was possible. Many of these methods including the bulk aerodynamic method, integral method, and profile method are discussed by Roll 2 (1965). With the evolution and development of sophisticated instrumen- tation and experimental platforms for use on the open ocean, accurate measurements of atmospheric and oceanographic parameters of scales ranging from millimeters to kilometers have become possible. As an outgrowth of the recommendations of the Joint Panel on Sea-Air 3, 4 Interaction of the National Academy of Sciences (1962, 1966) ' the Bardados Oceanographic Meteorological Experiment (BOMEX) was conducted during the summer of 1969. The principal objective in air- sea interaction was the study of the fluxes of momentum, sensible and 5 latent heat described by Davidson (1968) and Kuettner and Holland (1969). Current results from BOMEX have been summarized by 7 Holland (1972). Results of direct flux measurements from the research vessel FLIP obtained using the covariance or eddy correlation method and the well recognized difficulties of the measurement are 8 9 discussed by Pond et al (1971), Phelps (1971), Phelps and Pond (1971) and Leavitt (1973). The dissipation technique for 12 estimating momentum flux was used by Gibson and Williams (1969) from FLIP in 1968, and for sensible heat flux during BOMEX by 13 Gibson, Stegen and Williams (1970) and Stegen, Gibson and Friehe 14 (1973). " Experimental data for this thesis was obtained from measure- ments made from the Research Platform FLIP during a series of oceanographic cruises between August 1970 and April 1973 off the coast of Southern California. Mean and fluctuating component horizontal and vertical velocity, temperature, humidity, insti nt motion, and mean sea surface temperature were measured simultaneously. Fluxes of momentum, sensible and latent heat were obtained by the direct eddy correlation technique corrected for instrument/platform motions and compared with estimates of fluxes by the direct and inertial dissipation techniques. The influence of atmospheric stability on the determination of the fluxes by the latter two methods was determined. Latent and sensible heat fluxes were also determined using the. bulk aerodynamic technique (including stability effects) and compared to estimates of the turbulent heat fluxes by the direct covariance technique. 2. FLUX TECHNIQUES 2. 1 Direct Covariance Technique The optimum method of determining the turbulent fluxes of momentum and sensible and latent heat is to measure directly and appropriately average the covariances of vertical velocity with the suitable variable of interest. This method is known as the direct covariance or eddy correlation technique. The technique is based on the definition of the vertical fluxes as given by Momentum Flux T = - p uw S Sensible Heat Flux HQ = p C w 6 (1) b p Latent Heat Flux PL = L wq E v where u , w are the horizontal and vertical fluctuating components of the streamwise velocity vector U , 9 is the fluctuating component of temperature (° C) , and q the absolute humidity fluctuation 3 (jUgm/cm ). The constants are p density, C specific heat capacity, and L latent heat of vaporization. Overbars indicate v time averages assuming stationary flow. The covariances are obtained by integration of the appropriate cospectrum $ (where x is u , 9 , or q) between low and high frequency limits in the same manner as the variances of the individual turbulent components are obtained from the appropriate spectrum $ . The frequency range is determined to include all significant contributions to the integrals ■given by wx fi f h h = / * (f ) d£ and J" = f * (f ) df J, wx J XX (2; The low frequency (f^) or high pass cut-off is normally determined by removal of the record mean on data processing and is thereby set by the length of the data record. The low pass cut-off (f ) is h initially limited by the bandwidth limitations of the instruments used to measure the parameters u , w , 6 and q , and is subsequently set by low pass filtering during data analysis, usually adeqi;ate t'o determine the full value of the appropriate flux. Filters are used to reduce high frequency noise and minimize aliasing in analog to digital conversion. In this work the frequency range of the integration was -3 between about 1 x 10 and 10 Hz . Determination of the fluxes directly by this technique is fairly difficult in practice due to the effects of instrument platform motion Q on the measured turbulent velocity components. Pond et al (1971) obtained values of the covariance uw with the eddy correlation technique using a sonic anemometer to measure horizontal and vertical velocity from FLIP during Operation BOMEX. Employing an empirical correction procedure, significant corrections to uw were required to account for FLIP motion and effects on the flow field. Rotations of the principal axis of the Reynolds flux tensor were selected to make 1 /2 the spectral correlation coefficient R (f) = $ /($ $ ) uw uw uu WW ^equal to a value of -0. 5 for 0, 01 < £ z'/U < 0. 1 as suggested by 15' 16 8 Smith (1967) and Weiler and Burling (] 967). Pond et al found typical correction values for u\v were 13% per degree tilt and 5% and 3% per degree for wq and w 9 respectively, and it was felt that the measurements were within 1-2° of the correct coordinate system. Contributions to the u , w spectra and uw cospectra by wave induced FLIP motion were not included in the integration when determining variances and covariances. Despite the fact that no theoretical assumptions or approximations are required to employ the Q direct covariance technique, Pond et al assumed that there was no distortion of the Reynolds stress due to the large tilt angles calculated (~ 10° ) which would affect the correlation between u and w . 17 Kaimal and Haugen (1969) have found that the correlation ,,.. . uw . . , . coefficient r = , varies over a wide range irom near zero to uw a O u w -0. 5 , particularly under unstable conditions. This suggests that the spectral correlation coefficient R may also vary with stability. r uw 17 Based on results from the Kansas experiment, Kaimal and Haugen suggest a need for ± 0. 1° accuracy in the internal alignment and mounting of sensors used to measure the direct covariance (uw) in the atmospheric boundary layer.* For this research measurements of instrument platform tilt in the u , w plane were made using a vertical gyro located at a known angle with respect to the velocity sensors. Outputs of the vertical gyro were recorded simultaneously with the fluctuating velocity components and temperature and humidity fluctuations to determine corrected values of the covariances. Description of the instrument package and correction procedvires are contained in the instrumentation and data reduction sections. 2 . 2 Pis sipati on Techniques Both the inertial and direct dissipation techniques are somewhat advantageous over the direct covariance method in that they are much less susceptible to errors caused by instrument platfornl motion. This is due to the fact that the flux estimates are based on measurements of the small scale structure of the velocity and scalar fields. Three variations of the dissipation method differ in the technique used to determine the rates of dissipation of velocity or scalar variance are determined. The dissipation may be measured directly or inferred from the inertial subrange of the appropriate spectra or of the structure function. The technique for relating the dissipation of velocity and scalar variance to the fluxes of momentum and heat was first suggested by 1 8 R. J. Taylor (1961). This technique is based on the assumptions 19 discussed in Lumley and Panofsky (1964) that mechanical production is equal to energy dissipation at the same height in the constant flux layer for near neutral conditions, so that (production) -uw — = C (dissipation) (3) - 2 where € = mean rate of viscous dissipation = 2 v e.. , anc] P = (u . + u. .)/2 ; v = kinematic viscosity; p density, i»3 J*1 streamwise velocity, z = vertical height above the m and u and w are defined as previously. U m ean ean sea surface, The same assumption is made for the production and dissipation * of scalar variance, i. e. , s — x (production) -yw ~~ = -~f~ (dissipation) (4) r dz 2 where y and y represent the mean and fluctuating scalars (tempera- ture (T+9 ) and humidity (q+q)), X = mean rate of dissipation of scalar variance = D |grad y| , and D , the molecular diffusivity of the scalar. Assuming a logarithmic profile for velocity and the scalars, and implicitly invoking conditions of stationarity and horizontal homogeneity, we find — u , ~ dU * 2 — ,-, = — , u, = -uw (5) dz Kz dZ = ^ > y = . ?OL (6) dz Kz a * u ,. Where u;,, is the friction velocity, K is von Kar man's constant, normally assumed to be 0.4 , y the scalar scale, and a^~ (yw ^U/oz)/(mvh'/i)z) = K /K the ratio of eddy transfer / H m coefficients for the scalars and momentum, assumed unity for neutral conditions (Reynolds analogy). Also assumed is K °* K for humidity. Expressions for the fluxes can be obtained by combining equations (3) and (5), and (4) and (6) 2 , ~ ,2/3 u;;; = (K € z) (7) 2 a X z ?* ■ iff" « <8> 2. 2a Inertial-dis sipation technique 1 o Taylor determined values of £ and \ from the inertial 9 subrange of the second order structure functions for velocity and 20 temperature. From the similarity hypothesis of Kolmogorov (1941) 21 22 for turbulent velocity fields, and Obukhov (1949) and Corrsin (1951) for turbulent scalar fields assuming local isotropy, the second order structure functions in the inertial subrange are given by r _ 2/3 2/3 D (r) =[U(x+r) -U(x)] = a e r (9) uu • u 2 -1/3 2/3 DQQ(r) =[T(x+r) -T(x)] = bQ XqC r (10) where U and T (or humidity) are measured at streamwise separation TTT distance r , between L (energy scale) and 77 (dissipation scale). 3-1/4 77 is also known as the Kolmogorov scale, defined as (v /e ) Values of e and v can also be determined in the same y manner from the inertial subrange of the one -dimensional spectra given by * (k) = a 72/3 k"5/3 (11) uu u $ (k) = 0 x" e""1/3 k"5/3 (12) yy y y where a and B are universal constants assumed known, and the u y \_. radian wavenumber k = 2nf/U by Taylor's hypothesis. This technique requires accurate values of the constants a and B (or u y a and b ) , and the velocity and scalar spectra and structure u >' functions to follow the k ' (r ) form of the inertial subranges. In this work, examples of temperature spectra obtained from open ocean atmospheric data are presented which appear to exhibit a very limited, if any, -5/3 inertial subrange. Application of Eq.(12) to single frequency (wavenumber) measurements of the spectral function cotild lead to large errors in the estimation of sensible heat flux if an inertial subrange does not exist. Similar care must be taken ■ when applying Eq. (10) to single separation measurements of the Structure function. A substantial portion of the temperature spectrum should be measured (to — 100 Hz) to determine if a subrange does exist before this method is applied. Humidity spectra, appear to exhibit a -5/3 inertial subrange behavior over a wider range of frequencies (to ~ 20 Hz) than temperature 2. 2b Direct dissipation technique This technique involves measurement of the mean square values of time derivatives of fluctuating streamwise velocity and temperature to calculate dissipation rates directly. Direct estimates of e and x i'n the atmospheric boundary layer over the ocean from FLIP in 1968 and during Project BOMEX are described by Gibson and 12 13 14 Williams (1969), Gibson et al (1970) ' and Stegen et al (1973). Assuming local isotropy and Taylor's hypothesis (U d/dx = -d/dt), the viscous dissipation may be determined from the relations 7 = JUL /_$uf (13) and In practice the appropriate time derivative spectra are integrated to obtain values of the mean square time derivatives. Difficulties in this technique involve the high spatial resolution required of the sensing probes to nearly the Kolmogorov scale (77) , of the order of 1 mm in atmospheric flows. High frequency response (~ 2000 Hz) and very high signal-to-noise ratios are required in the .sensor and associated circuitry. At the present writing a humidity sensor with sufficient frequency response was not available to measure adequately mean square humidity time derivatives to calculate the humidity dissipation. As a result, the direct dissipation technique is applied only to estimates of the momentum and sensible heat fluxes. The direct dissipation technique does offer several advantages over the other techniques. Estimates of the fluxes require relatively simple instrumentation and data analysis, and are- not affected by sensor motion because of the high frequency response and fine scale spatial resolution of the sensors used. Measurement of spectra over the entire range of frequencies (wavenumbcrs) are readily obtainable to determine spectral shapes. The spectra combined with dissipation measurements provide a means of accurately determining the universal constants. 2. 3 Stability Considerations Application of the dissipation techniques using Eqs. (7) and (8) . does not account for effects of stability on the flux estimates. These equations are modified by consideration of the turbulent budget equations for kinetic energy and scalar variance, and the flux-profile relationships hi the surface layer, within the framework of the Monin- 23 Obukhov surface-layer similarity theory (Obukhov, 1946 and Monin- Obukhov, 1954). 24 In the first tens of meters of the atmospheric boundary layer, the fluxes of momentum and heat are assumed constant. Recent experimental support for this assumption has been given by Haugen 2 5 2C et al (1971) and Dyer and Hicks (1972). In this "constant flux layer, " according to similarity theory, the turbulence structure is determined by the surface shear stress 7 , the surface heat flux H o s the buoyancy parameter g/T, and z the vertical height. The latent heat flux H is included to account for humidity effects on buoyancy in the boundary layer over the ocean. From these parameters characteristic scales for velocity (u.,.) , and scalars [y = T , q,) are defined (as in Eqs. (5) and (6)). The length scales are z and the Monin-Obukhov length, defined as u,.3 T L = - - (15) Kg we v where the mean and fluctuating virtual temperature, T and 0 , as v v 19 given by Lumley and Panofsky (1964), include humidity contributions to buoyancy. They are written as T = T (1.0 + 0. 61 M) (16) v and 9 =- 9 + 0. 61 Tm (17) v where M and m are mean and fluctuating specific humidity (gm/gm). The scale L is a key independent variable of similarity theory and \determines the thickness of the surface layer above which buoyancy factors are not significant. Applying the scaling parameters to the vertical gradients of velocity and the scalars (temperature, humidity), Eqs. (5) and (6) are rewritten as rin u* ~ = -f- $ (z/L) (18) d z K z m * (z/L) . (19) dz K z a H r The functions 5> , the dimensionless wind shear, and $ , m H the dimensionless scalar gradient, are evaluated empirically. It is generally assumed that ?> = $ for temperature and humidity. H E 27 Monin and Yaglom (1971) conclude that the forms of <3? and <2? m H for unstable conditions (the prevalent condition over the open ocean) are best given by -1/4 $ = (1 - a z/L) for _1£Z/L£ 0 (20; mm *„ = (i - a z/D~1/2 (2i; rl iri A review of the constants a and cr has recently been given by m H 2 8 Busch et al (1973) and fairly good agreement appears to exist 29 for the value of a . Businger et al (1971) suggests a = 15 , m m 30 31 while Paulson (1970), Badgley et al (1972), and Dyer and Hicks 32 33 (1970) " find 0" = or = 16 . Miyake et al (1970) use a = a =16, m rl ni H also used by Pond et al, Phelps and Pond, and Eeavitt, to obtain results from BOMEX data. For neutral conditions = $ =1 \ m H 29 Businger et al (1971) find values of a = 1.35 and K - 0.35 as v compared to the often used values of a =1.0 and K = 0.4 , and y suggest or = 9 . 2. 4 Budget Equations If horizontal homogeneity and stationarity are assumed and the effects of humidity on buoyancy are included, the budget • ~2 ~2 ~~2 ~2 equation for kinetic energy per unit mass, e = u + w + v may 19 be written as (Lumlcy and Panofsky, 1964) - uw r — + -£- [w 9 + 0. 6 1 T wm ]-r - we - - r— p\v - e = 0 (22) 0 z — J2oz p 5k r The non-dimensional form of the budget equation is obtained by 3 multiplying Eq. (22) by K z/u and employing Eqs. (15) and (18) so that Eq. (22) can be written as <£>-z/L-D-D-$ =0 . (2 3) m e p e The terms represent the turbulent shear production, buoyant production, the flux divergence of turbulent kinetic energy, the flux divergence of pressure transport and viscous dissipation respectively. Three approaches to simplification of Eqs. (22) and (23) have been suggested. The first approach, given by Eq. (13), is the assumption that production and dissipation of mechanical energy are equal for near neutral conditions. For |z/L j < 0. 5 Busch and , 34 Panofsky (19oS) suggest that dissipation is balancec by the sum of buoyant and mechanical production, and that the flux divergence terms may be neglected so that Ecj. (23) simplifies to $ - z/L = $ . (24) s € 35 McBean, et al (1971) conclude from, measurements over land that for near neutral conditions (|z/L | < 0. 2) Eq. (24) is a good approxima- tion. However, for more unstable conditions, - z/L> 0. 3 , dissipation appears to exceed prodiiction, and for z/L ~ -0. 5 the sum $? - z/L - <3> is about 30% of shear production and more than half m € 33 8 of buoyant production. Miyake et al (1970) and Pond et al (1971) apply Eq. (24) to calculate momentum flux, however, they do not include stability effects on the mean velocity profile as given by Eq. (18). Hicks 36 and Dyer (1972) include buoyancy effects from Eqs. (18) and (24) to calculate the momentum flux by the inertial dissipation technique. A recent approach to simplification of the turbulent energy budget 37 has been suggested by Wyngaard and Cote (1971) based upon \ measurements in the surface layer over land. From measurements of 2 • 2 we at three different heights the turbulent flux divergence of e was estimated and found to approximately balance buoyant production in the stability range - 1.0 S= z/L £ 0 . Eq. (23) reduces to bU uw + € + I =- 0 (2 5) 0z v ' where the imbalance I , is attributed to pressure transport divergence. Under stable conditions the imbalance may not be substantial and under strongly unstable conditions (z/L = - 2) dissipation and total production did balance. Empirically, the expression for the imbalance term is written as 3/2 ^-| I = (1-15 z/L)"1/4 - (1 + 0. 5 | z/L |2/3) (26) u., where the first term on the right-hand side is the Businger formula for dimensionless shear production (Eq. (20), 0" = 15 ), and the m second term is the empirical expression determined by Wyngaard and _ ,37 . . , Cote for unstable dissipation data. Using this approach, momentum flux corrected for stability effects may be calculated using the empirical expression for unstable dissipation written as KZC = (1 + 0.5 | z/L |2/3)3 2 . (27) 3 u,. This expression for the dissipation was employed by Stegen et al 14 (1973) to calculate momentum flux by the direct dissipation technique. In recent work employing data from Operation BOMEX, Leavitt (1973) found that total production approximately balanced dissipation in the stability range - 0. 2 5 z /L a -1.5, and that dimensionless turbulent transport as estimated from measurements at two heights was only about half of the dimensionless buoyant production as measured by 37 Wyngaard and Cote (1971). In general the budget o£ temperature variance (9 ) may be 27 written (Monin and Yaglom, 1971) beZ 4. ~ b®2 7 — q &0 + I a2 r» + u. : + Zu-6 + t 1 u.9 - D. 6 t i 5 x. 1 6 x ■ b x. 1 l e b x. 2D (SL, + 26R' + ux + s 0 bx. C ( i P (28) where repeated indices are summed and u and x may be replaced i l by (u , v , w) and (x , y , z) respectively. Here 0 is the mean potential temperature. The temperature variance budget can be simplified by invoking the assumptions of stationarity and horizontal homogeneity; Eq. (28) can then be written as bz 26z 2 9 C 0 where the dissipation of temperature variance x is defined as xe el5x.j i (30) In a similar manner, the budget of humidity variance 3 R written as (Coantic and L,educq, 1969) (q ) may be is. + u. bq 6t j b i 2 u.q 6q j 6x. bx. u.q J D 6q q bx. 2D M-) + S q bx. q (3i; which simplifies under the same assumptions of stationarity and horizontal homogeneity to wq t 6q 16 2i — c-n T^1" + r- t wq +iy b„ ~ u 6z 2 b z 2Xq (32) and the dissipation of humidity variance is defined as X 2d M q bx. J (33) The first three terms of the simplified budget equations for tempera- ture and humidity variance (29) and (32), represent production of scalar variance, transport of scalar flux divergence, and scalar variance dissipation due to the smoothing action of molecular diffusivity respectively. The temperature variance budget contains additional source or sink terms not included in the humidity budget. The term 2 8R represents the effecis of heat transfer due to radiation 2 9? on the temperature variance, the effects of viscous dissipation on CP the temperature field due to the internal friction of thle fluid, and S 9 3.nd S represent generalized source or sink terms t q o account for any phase changes of water vapor or interactions of the temperature and humidity fields due to radiation. 27 39 Monin and Yaglom (1971) and Plate (1971) suggest.by hypothesis that the viscous internal heating term 29€/c is insignificant 40 and may be neglected. Friehe (1973) suggests that this term may not ,du* be negligible and that there may be a positive correlation of G € due to an increase in 9 produced by local, rapid adiabatic heating by viscous dissipation. Although a mean value for viscous dissipation € may be estimated from the mean square of the velocity derivative (-— •) d t du2 (see Eq. (13)), a positive correlation of 9 (-77) may not accurately reflect the actual correlation between fluctuating temperature and the instantaneous viscous dissipation Qe ; (- — ) is only one component of dissipation, used to calculate 6 by the assumption of isotropy. In general, the effect of radiative heat transfer is to reduce the 41 value of the mean square temperature fluctuation (Goody (1956), 42 39 Townsend (1958), Plate (1971) ). For internal radiative transfer 42 . 2 Towns end indicates that maximum destruction of 6 occurs at very small scales of the temperature fluctuations since the most pronounced radiative transfer occurs over the shortest path interval. For atmospheric conditions with high humidity content and strong that more absorption of long wave radiation occurs at larger so: radiative transfer, Phelps and Pond (1971) suggest lies resulting in a more homogeneous large-scale temperature field and suppression of 39 low frequency temperature fluctuations. Plate also indicates that partial absorption of long-wave radiation by atmospheric water vapor could cause a change of state-,, (conversion to sensible heat) which would influence the temperature field., It is not clear whether this absorption and change of state of water vapor would act as a source or sink in the temperature and humidity variance budgets, and could be included in the generalized source terms. 43 Coantic and Seguin (1971) have shown that radiative flux divergence due to absorption of infared radiation (long-wave) by water vapor and carbon dioxide always acts in such a way to increase the absolute value of the turbulent heat flux. They conclude that the constaiit heat flux hypothesis for the surface layer may not be valid, especially for conditions of moderate wind and high moisture content, even for heights above 1 meter. The generalized source term may also include the effects of ocean spray on the temperature and humidity fields and possible connective conditions in the upper boundary of the surface layer as suggested by Phelps and Pond (1971). To further simplify the budget equations of temperature and xe et al (1970),"'' humidity variance it has been common practice (Miya Hicks and Dyer (1972), Pond et al (1971), Phelps and Pond (1971), 10 3 7 13 Wyngaard and Cote (1971), Stegen et al (1972) and Paulson et al 44 (1972) ) to assume production of scalar variance is equal to the dissipation of scalar variance (Eq. (4)). Neglecting source terms in the temperature variance budget and assuming the transport terms may also be neglected Eqs. (29) and (32) reduce to and -w9dT=2xe (34) i - - wq — ^ = - X • (35) d z 2 q 1 8 R. J. Taylor (1961) justifies the assumption of production of temperature variance equal to the dissipation based on negligible values 1 2 of the flux divergence term — C P w 6 and the viscous heating term 2 p — 45 6 € as compared to the production term. Panofsky (1969) also suggests omission of the transport term in the temperature variance budget and that in general, this term is of the order of 10% of the production or dissipation terms. Similar results were obtained by 37 Wyngaard and Cote' (1971) based on measurements of the transport 37 term over land. Wyngaard suggests that the transport term is an order of ma.gnitude smaller than the production for moderately unstable conditions -is Z/LS 0 . Recent studies by Leavitt (1973) and results presented in this work indicate that in the: atmospheric boundary layer over the ocean, dissipation of temper- ature variance can greatly exceed production for moderately unstable conditions, Leavitt finds that the mean value of turbulent transport in the temperature variance budget is about 2 5% of the production (representing a loss) for .25 ^ - z/L £ . 75 and a trend similar to .37 Wyngaard' s , suggesting that for highly unstable conditions the 46 transport may become a gain, supporting Deardorff's (1966) suggestion that for a counter-gradient of potential temperature, positive heat flux can be supported due to turbulent transport. \ 3. INSTRUMENTATION AND DATA ANALYSIS 3. 1 Experimental Arrangement Data for this thesis was obtained from measurements made from the Research Platform FLIP during a series of oceanographic expeditions in August 1970 (SOMA), September .1971 (MITOS I), February 1972 (MITOS II), April 197?- (MITOS III), and April 1973 (OWAX). For each cruise FLIP was towed to an operating area in the vicinity of 31°40' North latitude, 118° 00 ' West longitude, approximately 60 miles west--, of Ensenada, Baja California. After a stable vertical position had been attained, FLIP drifted freely with keel orientated upwind. "Wind direction during each cruise was predominately out of the north and northwest so that open ocean conditions were achieved. The configuration of FLIP employed for the MITOS III and OWAX cruises is shown in figure 1. In this configuration an instrument package was located at the end of the 18. 3 meter port boom. The 10. 7 meter starboard boom was used to mount a fixed and a trimmable sail to maintain FLIP in an upwind orientation and compensate for the drag on the port boom. The instrument package used for measurements of turbulent velocity, temperature, humidity, and instrument motion is shown in figure 2. It was possible to mount the package rigidly at the boom height of 12. 5 meters or to heights 24 FIGURE 1 Research Platform FLIP in the stable vertical position, with 18 meter port boom and compensating sails on starboard boom i I . kV I J ill f' v VU ... V >_U- J, ,'/ ...A; i 't,! f • - I ! II i — *%" f 0 a lil 8- I J- 1.6. 5. 114(j) i t' ■ / • / 1 i 1 ■ 1 ■<■.;< 1 ' I ■ ( t t 1 1 , V 1 'i >■/ 1 I i • . ' i 1 1 1 I .,4 FIGURE 2 Instrument package for flux measurements [w^.^i^:,w.T-.^TL^^^^j^i^i»w»rT?w^ ' * iM^wys^rwi!^ W, 0. 25 ma) . Absolute fluctuation calibration of the instrument s for the last three cruises was probably better than 10% . The frequency response ,of the humidiometer appearedTo be flat out to about 5-10 Hz . Measurements of mean air and sea surface temperature were made with precision Hg thermometers and Hewlett-Packard Model 280 1A Quartz thermometers. The quartz thermometers were employed only in the MITOS III and OWAX cruises. Mean temperature data from the MITOS III cruise indicated that the exposed quartz thermometers were subject to radiation heating. For the OWAX cruise the thermom- eters were equipped with aspirated spirated radiation shielding. Absolute lumidity was determined from measurements of dry and wet bulb air emperature using a sling psychrometer. Dew Point temperature was lso measured with a Cambridge Systems dew point hygrometer. 39 3.2c Velocity measurements Fine scale velocity measurements were made with linearized constant temperatixre anemometers and hot-wire, x-wire or hot-film sensors. The anemometers were purchased from Thermo Systems Incorporated (Model 1054) and DISA Electronics (Model 55M01). The straight hot-wire, x-wire and hot-film sensors Jere also purchased from TSI or DISA, constructed of platinum or tungsten, and from 0. 4 mm to 1. 25 mm in length with frequency response out to 1. 5 KHz or better. The hot-film sensors were constructed of a 0.025 mm quartz cylinder over which a 0. 5 mm long platinum film was plated with gold leads to the film. During the first three FLIP cruises, precise measurements of horizontal and vertical velocity with the x-wire sensors often were not obtained due to excessive (~ 30% for MITOS I) drift of the probe calibration in the wind field. The primary source of the calibration drift appeared to be contamination of the hot-wires by salt spray. Use of the hot-film sensors during the last two cruises greatly improved the fine scale velocity measurements and sensor calibration drift was not a significant factor. A three-component sonic anemometer was also used for velocity measurements during the last two cruises. For the MITOS III cruise (April 1972) an EG&G sonic anemometer was borrowed from Rome Air Development Center for velocity measurements over a band- 40 width from DC to about 10 Hz. Measurement of velocity with this instrument is based on the principle of Doppler-shift of sound waves by the flow field in the measuring path. Since the instrument is an absolute sensor no calibration was required on FLIP. Unfortunately, ad-out circuitry ty data was due to a failure of a portion of the EG&G associated r: only a limited amount of horizontal and vertical veloc obtained during the cruise. For the OWAX cruise, a similar EG&G three -component sonic anemometer was purchased, and the sonic anemometer readout system was designed and built by Tom Beaton and Mark Barnum at UCSD, This instrument and readout circuitry were thoroughly tested and calibrated in the 30 inch square, low velocity wind tunnel at UCSD up to a maximum wind speed of 20 meters/ sec, and was successfully used during the OWAX FLIP cruise. Some minor distortion of the vertical sensing path of the sonic anemometer was discovered during the testing and calibration procedures. This distortion was due to a slight misalignment of about 1. 1° between the vertical sensors but was corrected for in the calculation of momentum and heat fluxes during subsequent data analysis. Mean velocity during the cruises was also measured with Teledyne-Geotech precision cup anemometers and associated readout circuitry designed and built at UCSD. The cup anemometers were also calibrated in the UCSD wind tunnel and used for comparison to the nean velocity obtained from the sonic, x-wire and hot-film sensors. 41 3. Zd Analog instrumentation The analog instrumentation employed during the FLIP cruises and for data analysis consisted of analog monitoring, processing, record ?md playback equipment as shown in figure 3. Data signals were conditioned for FM analog recording by means of ampli- fication and filtering to achieve desired signa] levels. Several techniques were employed to improve signal-to-noise ratios and optimize the dynamic range of the tape recorders. These included the use of pre-emphasis (de-emphasis for playback) circuits designed and built by Tom Deaton, and Tektronix 3A8 operational amplifiers as differentiators for analogue pre -whitening of fine scale velocity and temperature signals. Buck and gain amplifers designed by Bruce Williams at UCSD were used for removing known DC levels and subsequent amplification of the bucked signals. The 3A8's were also used for signal amplification. Burr-Brown sum and difference amplifiers were used to obtain horizontal and vertical velocity data from x-wire probes, and also for removing tape recorder flutter noise during playback when necessary. Krohn-Hite and Hewlett-Packard filters with cut-off rates of 12, 24, and 48 db/octave were used to minimize any high frequency noise contamination. Signals were sent through a multiplexer /demultiplexer circuit or directly through a calibration and input selection patch panel for recording on FM analog tape. The patch panel could be used to select either data or calibration 42 signals for recording, and also used as a signal input monitor terminal during recording and playback. Two types of tape recorders were used for FM analog data recording. A Sangamo 3500, 1/2 inch, seven channel FM tape recorder was employed for the first four cruises, and a Honeywell 7600, seven/ fourteen channel, 1 /Z inch/1 inch FM tape recorder for the OWAX cruise. Both tape recorders were adjusted for a 50 db signal-to-noise ratio with a 1 KHz, 5 volt peak-to-peak sine wave. Allowing for signal intermittency and discrete amplification factors available, data signals were recorded as close to ± 2. 5 volts peak level as possible without overranging, so that typical signal-to-noise ratios for the data tapes was approximately 40 db. Overload lights on the input selection panel and Krohn-Hite filters, as well as Tektronix storage type oscilloscopes or chart recorders, permitted constant qualitative monitoring of input data signals. A hard-wired Ubiquitous Spectrum Analyzer with oscilloscope and/or x-y plotter output could be used for on-line checks of input signal frequency content and spectral shape. The spectrum analyzer was also used as a valuable tool for determining noise contamination of signals which would have otherwise gone undetected. 3. 3 Data Processing An IBM 1130 digital computer system was employed for data reduction and subsequent data analysis of the analog tapes recorded on 43 FLIP. A detailed discussion of the laboratory computer system at TJCSD and various digital techniques employed for turbulence analysis 47 49 is given by Gibson (1973) and Clay (1973). Analog- to -digital (A-D) conversion was accomplished -with a data acquisition interface to the computer permitting 15 bit samples at up to 100 KHz for single channel operation. Multiplexed sequential sampling of up to 8 channels was also possible at correspondingly slower sampling rates. Digital data could be stored on a 500K data storage disk or on digital tape using a Datum Model 100 digital tape drive unit. The computer system also included an IBM 1442 card reader /punch and a Calcomp 565 plotter for displaying results. A high speed stand-alone digitizer /data logger system was also developed for A-D conversion shown schematically in figure 4. This system consists of a Tustine Electronics AD 1500 A-D converter- multiplexer, a data buffer, digital oscillator and control circuitry, and a Kennedy 8109 digital tape drive unit. The advantage of this system was that it could be used for double buffered "gapless" sampling at up to 8 KHz for one channel operation or at correspondingly slower rates for up to 16 channel operation. By "gapless" sampling is meant that there was no time delay in sampling the data caused by writing that data on tape. It was then possible to concatenate several tape blocks to make one computer record when analyzing tapes from the data logger system- Computer records consisted of up to 2048 words depending on the number n FIGURE 4 High speed standalone data logger w -*•- — ~*^ y ' /^^ V f\ W > / \ 1 1 ft >— i ) ^ ) < p* V / ' \ / H Q 1 J . W H w * < \ h < •P 1 ^ z o ffl . I < h , 1—1 C H 2 o u tf i rt o i w 0 4 rt & o < w 1— 1 1-1 -< > J D S ^ < D1U1 CON AND • i I j > i » o co 0 i-l j < <; 'A £ 0 < CO w o o o < <: Q p w w ft CO X o I— I H r- 46 of channels sampled (typically 4) and the type of analysis programs used. An extensive, integrated group of time series analysis programs was developed by Gene Dial and Jerome Dayton for analysis of the turbulent data and plotting results. The majority of turbulence data analyzed was input from digital tapes, however, some of the earlier results were obtained from data stored on disk. Figure 5 shows a block diagram of the time series analysis system with programs grouped according to their primary functions: data collection, analysis, 47 and display.. This figure is also originally from Gibson (1973). The data collection programs are used for digitizing operations to transfer data from the A-D interface to tape or disk, and for data transfers between tape and disk. Analysis programs permitted examination of raw digital data, statistical analysis, and spectral and cospectral analysis using fast fourier transform techniques. The display programs could be employed for a variety of functions to organize and output analyzed data. A-D conversion consisted of amplification and filtering of the played back analog signals to make maximum use of the dynamic range of the A-D converter (± 10 volts) or data logger (± 2. 5 volts), and prevent aliasing of the output spectral data. Input analog signals were filtered at the Nyquist frequency, i. e. , at half of the sampling frequency. The analog instrumentation described earlier was used for FIGURE 5 Time series analysis system DATA OLLECTIOlM ANALYSIS DISPLAY DATAP| ana log data to dis. tape DATlNl analog data to disks AMES tape| disk data to digital tape RSTA7T record statistics MOMNITf statistical moments CHCOR rorrclatic Tit ME Series Ana^^^Jystem Sept 1973) 1.6.4.75 XRAWDJ Jata to (typewriter [disk, cards T STHSTJ histograr COSPCJ cospectrun u SETUpf power spectrum. IsapT structure functions CPLOT time scries plots FINDBI locate records w /spikes SQVAL|" square a time PLNLN| linear- linear plot EL-GLGJ log-log plot PLNLGJ lin-log plot punch cards IRANSR] read cards 3lgln| 1 log-lin L plot RCPPsJ read cards RCDDT read cards AREA [ integrate FMUL | re- calibrate FEDITl selection POLYl smothj polynomial curve fit curve smoothing HAMM| HANN| Hamming - Ila lining RATIO| plotdJ ratio o£ two curves draning aid 49 this off-line analog signal conditioning. The digital tapes were initialized with an alphanumeric tape label at the beginning, consist of many tape records in the middle, and have an end -of -file mark at the end. Specification of the number of channels of input data and the record length was made by control communication to the digitizing programs DA TAP and DA TIN through the computer keyboard/type- writer. Several realizations over one section of analog data were normally made at different sampling frequencies and corresponding filter frequencies so that spectral estimates could be obtained over a wide range of frequencies. The primary analysis programs employed for this work included CPLOT for time series plotting and determination of calibration factors; the statistics programs STHST and RSTAT used for calculation of averages, variance, standard deviation, running mean, and max- imum and minimum, values, and CHCOR and MOMNT for calculation of correlation coefficients and multiple channel moments or covariances; the spectral programs SETUP and COSPC were used for calculation of power spectra and cospectra. The SETUP program included options for boxcar or triangular data windowing and digital pre-wbitening/post- darkening. For analysis of signals with steep power spectra and high power at lower frequencies (particularly true for horizontal velocity data) the triangular windowing was found to minimize the possiblity of "leakage" from lower to higher frequencies. Turbulent velocity and 50 scalar spectra fall off at a rate of slightly less than 6 db/octave. Predicted slopes for log-log plots of turbulent velocity and scalar power spectrum versus frequency would be -5/3 as given in Eqs. (11) and (12). The boxcar window employs a direct transform of the time series while with the triangle window the data is multiplied by factors increasing from zero to one at both ends of the data record to the middle. This means thtit much less energy is transferred from high to low frequencies in the convolution operation employing the triangular window since the side lobes of the triangle window fall off at 12 db/ octave rather than 6 db/octave. Another means of reducing leakage was to flatten the signal spectrum from -5/3 to a +1/3 slope by analog differentiation or by digital pre -whitening (i.e. transforming the first difference of the digital data). Effects of leakage on atmospheric velocity data from the MITOS III cruise and subsequent techniques to minimize the leakage are illustrated in figures 6a, 6b, 6c, and 6d. A velocity signal from the hot-film and its analog derivative were simultaneously sampled at 50 and 500 Hz to obtain several hundred 1024 point records which were transformed and averaged. Figure 6a shows effects of leakage on the boxcar window transform of the "straight" signal. The spectral estimates were multiplied by the corresponding frequency (f) raised to the 5/3 power before plotting. Sampling at the two different frequencies FIGURE 6 Illustrations of techniques for minimizing "leakage" in spectra a. Box car window transform, leakage b. Derivative pre -whitening c. Digital pre-v/hitening d. Triangular window transform 52 VELOCITY SPECTRA <*" in o , V! 1 -tr. AwwWo-^ BOXCAR WINDOW LEAKAGE 10 ' 10 " frequency ' '""'lb1 io* "o DEHYIAT1VE f'1" b. \ 1 1 V a B B. a a DERIVATIVE PRE WHITENING . it Tn i or '• ' ' ' i'o ' '"ib° ' '"ib" 10 POWER SPECTRA Of VELOCITY SAMPLED AT SO HZ 1.4.7.7! AND S"0 HZ W,T11 BOXCAR "ATA WINDOW FREQUENCY POWER SPECTfr-W OF VELOCITY DERIVATIVE SAM1 LED AT SO AND S00 HZ WITH BOXCAR DA I A WINDOW |,t,7.&9 *o ti?o w- VXLOCfTY SPECTRA t V^^^/w^r^ DIGITAL PREWHITENING 10' TJL* 5PICT"A °' "CLOriTlf SAMPLED AT SO HI I *™„ HI W|™ » ''KVITAI. I.F.WHITtNINO ? i E VELOCITY SPECTRA I /\^J^&f"~<< TRIANGULAR WINDOW -&■ ib" ib" ib' ' ■ " > MSOMCffCf POWER SPECTRUM Of VELOCITY SAMPIIP AT *0 HK AND S60 Hi WITH TRIANCULA.A DATA WINDOW 1,1, T.TI 53 accentuates the leakage problem for the high frequency run since the low sampling boxcar window is wider in time and narrower in frequency, so there is less low frequency leakage in the overlap region of the two spectra. Figure 6b shows the effects of analog differ intiation of the signal with a boxcar window transform. Spectral estimates were multiplied by f raised to the + 5/3 power before plotting. Due to the low energy of the derivative spectrum at low frequencies there is little energy leakage to higher frequencies and consequently good agreement of the high and low spectra hv-the overlap region. The fall off of the high end of the low frequency spectrum is due to filtering. Figure 6c shows the effects of digital pre-whitening/post-darkening (correcting for the effects of the transfer function of the differencing operation) of the straight velocity signal with the boxcar transform. Results are similar to that of the analog differentiation pre-whitening. Figure 6d shows the straight velocity signal transformed with the triangular window and the spectral estimates multiplied by f raised to the 5/3 power. Again there is very good agreement in the overlap region. Due to the time consuming nature of the digital pre-whitening technique, the triangular window transform or analog differentiation was employed for minimizing the effects of leakage during spectral analysis of high frequency data. Spectra computed with the boxcar window at sampling frequencies below 100 Hz did not appear to be greatly affected by leakage. However, any leakage effects were minimized by 54 obtaining several realizations of spectral data at different frequencies and matching the high frequency spectra to the low frequency spectra. Reduced data from the analysis programs was initially stored in (x,y) lists on a special disk file where it could be modified for plotting or output to punched cards. The plotting routines consist of log-log (PLGLG), semilog (PLGLN), and linear-linear (PDNLN) coordinates. Data could be calibrated before analysis by entering the appropriate computer units per physical units into the analysis program or by modification of the output data with the FMUL program. The FMUL program allows recalibration of the x,y lists by specification of the variabie-s A, B, C, D according to the formulae: ,B ,D (new x) = A * (old x) v (38) (new y) - C * (old y) * (new x) Recalibrated values of x and y replace the old values on the disc file allowing for output data of the type shown in figures6a-d. The special disc file may also be reentered by inputing saved data cards with the card read programs RANSR, RCDPS, and RCDDT, each program, applicable for a different data card format. 3. 4 Velocity Pitch Corrections Data obtained during the MITOS III and OWAX cruises was used to calculate the turbulent fluxes by the direct covariance technique corrected for instrument tilt. During these two cruises optimum 55 ! experimental conditions were achieved, thus making this calculation possible. The instruments were mounted at the end of the long port boom 18 meters from the side of FLIP which substantially eliminated the strong tilt effect experienced during Operation BOMEX. Dirft of horizontal velocity sensors experienced during the first three cruises was substantially eliminated using the hot film velocity sensors. The sonic anemometer was employed for limited horizontal and vertical velocity measurements during the MITOS III cruise and for more extensive measurements during the OWAX cruise. The pitch compon- ent of the instrument package due to FLIP motion was measured with a vertical1 gyro system developed by R. E. Davis of Scripps Institution of Oceanography and used to convert measured vertical velocity for this data during digital analysis. The vertical gyro was calibrated in the laboratory prior to the FLIP cruises and mounted on the instrument package so that its axis was exactly parallel to the vertical axis of the sonic anemometer. Calibration of the pitch gyro was possible to 0. 1° using a specially constructed tilt platform, also used for the sonic anemometer calibration. To correct for instrument platform tilt, the measured horizontal and vertical velocity components were rotated in the x-z plane by an amount equal to the pitch angle measured by the vertical gyro. This correction is not relative to an inertial reference frame and as such does not correct for all components of FLIP motion, but only for 56 instrument tilt due to FLIP motion. It was also necessary to correct the measured vertical velocity data from the sonic anemometer employed for the OWAX cruise due to a misalignment of the vertical sensing path heads by 1.1° . Denoting the measured and corrected velocity components by u , w and u ,\v respectively, and making a positive rotation of mm c c ° c the vertical axis in the downstream direction by an angle

cc mm mm s ' (39; 2 2 w sin epeos

ffi CO IT. o C in o u in »H CO M ~ in u c &■ M o — qj •i-< tr •H T3 C o O U U 3 — a 3 ni pq <3 a; H H H H U 1h O ^ £* • r-t > _ d ID W g X tr> >! 4J vj ■h O *■« O c *o « e W m < 3 c o o u a at Pn •H-' E o o o o o o *~ O 60 e e < u &■ > x£ -fa °- : l?E ISIS. If *5 FIGURE 7 MITOS 1-1 time series, u, w, T, q signals measured simultaneously, 12 minutes of continuous data 62 ■ 1 1*3 © £ *s: =^ > J . ■*. _?■ i s 1 _3£ u _ I S I • o ^ r~ ^ — rt -I ' 6 I « FIGURE 7 a. First "magnification" of MIT OS I time series (x5), 2. 5 minutes of data 64 - r Q © © ^ X ■^ S- 3^ 7 I _i- -d -■—■£—■ 3 KH I-l-M H-l-I-l! FIGURE 7 a. 1 Second "magnification" of MITOS I time series (xlOO), 14 seconds of data © n**-' 3 ^f^kt^^e^ :»*>ERATi.*fi: T JO'C 1 M^^fxy flTICAL rtiocrrr T » h ?wrmt*f,r N^> rt *d W /^\|k «' f ^^wWVU^w*1 •*■ ^S** RI?ONTAL VELOCITY U T | 1..C 1 ' 7J0(m ^A*.^ ^ Wt^W ©• -^ K*i»a ^A'/N\A^- v^^\M^V^ V — 1 l«C — TiOem T -1- A ,V< )^vvrvivjr»w FIGURE 7 a. 2 Third "magnification" of MITOS I time series (x50), 28 seconds of data T , -4^M^ i.MAM i VERTICAL VELOCITY W T l Im'MC T 1m/l*C o w y^\ y^vr VAm/"" I^Wt^t-^- — IU k rt^ M K w IT1 M^>W .. , y ■^f 1 i Jl . Fr*"1' [■ 1 lac \ ■ — 7m«ttr»- !^*\fetf^^ AA^MI^ ,\/Vv¥\v v'VAVw / A^^-^w^ (AZ) cont. humid / \* T i ^ty %f i WiTv v^H *'Z0HTAL -I 1HC ) aoair 69 time series is the pitch angle measured by the vertical pitch gyro on the instrument package. For each cruise the time series begin with the large scale structure of each signal and show successively smaller scales of the original time series. The gyro pitch is only shown in the largest scale time series for OWAX data. The procedure employed for the time series analysis can be compared to increasing the magnification power of a microscope to look at smaller scales of any particular feature of the object. Measurements of absolute humidity during the MITOS I and OWAX cruises were made with the Lyman -Alpha humidiometer so the response in both cases will be similar. Temperature was measured with a platinum cold wire for the MITOS I (figure 7) and OWAX 4 (figure 9) data and with a micro-bead thermistor for the. OWAX 2 time series (figure 8). The temperature signal for the MITOS I cruise was high- pass filtered at 0. 001 Hz (6 db/octave) so that events occurring over a period greater than the time constant of the filtering process (159 seconds) will be attenuated. For this reason the period of time covered by the first figure of the MITOS I series (figure 7) is of smaller scale than the first figure of the OWAX 4 series (figure 9), but can be compared to the OWAX 2 data presented in figure 8. Horizontal and vertical velocity for the MITOS I data was measured with an x-wire anemometer, while the horizontal and vertical velocity measurements for the OWAX data were made usin" a ^ s FIGURE 8 OWAX-2 time series, u, w, , T, q signals measured simultaneously, 8. 5 minutes of continuous data \ 71 •ds .2. > %- -J _§ 'S _J ■^ -e 1 < _,J5 s ^> .Jit :3L -£: 5^- I- I- tf h-H IrHH |fi-n 72 sonic anemometer. Limitations of the frequency response of the sonic anemometer as compared with the x-wire can be seen for the smallest scales represented in OWAX figures 9bl and 9b2. It should be noted that the ccnterline of each time series does not necessarily correspond to the zero or mean level of each individual signal. The large scale trends in the MITOS I and OWAX data are shown in figures 7, 8, 9 representing 12, 8. 5 and 54 minutes of data respectively. In general, ramp-like structures of 100-200 m wave- lengths can be seen in the temperature and humidity signals with warm humid air associated with upward vertical velocity and negative horizontal velocity changes. Both the temperature and humidity rise gradually to a maximum value and then decrease sharply to a minimum value. The gyro pitch angle is in general out of phase with the horizontal velocity variations and in phase with the vertical velocity variations, with positive gyro angles associated with larger upward excursions of the vertical velocity. Referrring to the first "magnification" of the time series in figure 7a and 9b representing 3 and 3. 5 minutes of real time, the ramp-like structure of the temperature and humidity signals can clearly be seen. The temperature signal for the MITOS I data is o more like the BOMEX temperature signals presented by Pond et al and Leavitt. The original filtering process should not have any significant affect at this scale for the MITOS I data. The humidity and temperature FIGURE 9 OWAX-4 time series, u, w, cp , T, q signals measured simultaneously, 54 minutes of continuous data (

f- — tf-H U UJ > > H Sf o FIGURE 9 b. First "magnification" of OWAX-4 (xlO), 5. 4 minutes of data T | Wuiir • ©h T* Tii 17/L'TI" i— #IAW^i.' -ill ! Vw ERATUfJ „,„ w / I'1' IP ;rtical ELOCITT | -25mc- I30m«ton 1*1 I. f^vy^^v^A^ . ^.w^aa. 'iV vy ®eonl. T 3 ^Bin/cm* 1 T = -JO'c 1 fHTiCAL tUOCITY v4t . in/ Oil At* n./1'" i V 1 "'id /^ ' 130 T..ii.i FIGURE 9 b. 1 Second "magnification" of OWAX-4 (x200), 16 seconds of data T 3 V"^ .gm/ero* V"7" ~ ^vTV") v^AOp^I f . ^^^^104^ FIGURE 9 b. 2 Third "magnification" of OWAX-4 (xlOO), 32 seconds of data KUMIOITY Q T , T .JO'c 1 VERTICAL VELOCITY Li i' tWiZONTAL VELOCITY -L T lm/tte 1 ■UMIDITY 0 T ! UW lAA^ ■\J We cold f iyfe* JL L^ 1 1 Jw\« mrrWW* 81 ramp interfaces are not only associated with maximum valxies but also with minimum values of temperature and humidity and with what has been termed "cold spikes" in the temperature signals. The cold spikes appear to be more pronounced in the MITOS I temperature signals than in the OWAX temperature signals. The OWAX temperature arid humidity signals appear more intermittent than the MITOS I signals, even though the height of the sensors for the OWAX data was 350 cm as compared to 500 cm for the MITOS I data. From concurrent research on BOMEX, MITOS I, MITOS III and OWAX data McConnell 50 s (1974), has obtained kurtosis values for dT/dx from MITOS I and BOMEX which are lower by a factor of 2 than similar kurtosis values calculated for OWAX and MITOS III data. This indicates more intermittency in the temperature data for the later cruises. Figures 7al and 9bl show the smallest scale magnification and each represent approximately 12 seconds of real time. The ramp-like structure of the temperature and humidity fields is still evident at this scale at wavelengths of less than 5 m . The temperature and humidity appear well correlated except at the interfaces of the ramps where the largest cold spikes in the temperature occur. Figure 9bl shows that cold spikes can occur during relatively quiescent periods between the large scale ramps. There is relatively more activity at higher frequencies and more small scale ramps for the MITOS I data as compared to OWAX data. Another feature peculiar to the temperature 82 signals for both OWAX and MIT OS I data is the occurrence of revei se ramps at scales less than 500 cm . These reverse ramps showing interfaces reversed to the mean flow direction are similar to the large scale ramp structure of temperature in a heated jet as discussed by 51 Gibson, Friehe and McConnell (1974). The reduction of frequency response for the sonic anemometer as compared to the x-wire can be seen in figure 9b 1 and 9b2. Figures 7a2 and 9b2 show the existence of cold spikes at ramp interfaces occasionally on the upwind reversed interfaces, and also during more quiescent periods. The OWAX data show more inter- mittency than the MITOS I data and the occurrence of reverse ramps is in evidence. The MITOS I temperature signal also exhibits a slower warming trend after an interface in which the temperature decreases than the OWAX data exhibits. The effect of intermittency of the OWAX temperature data and the effect of the different behavior of the OWAX and MITOS tempera- ' ture signals at larger scales on spectral and cospectral shapes will be discussed in Sections 4. 5 and 4. 6. Differences between temperature spectra and sensible heat flux cospectra are similar to those obtained by Pond et al, Phelps and Pond, and Leavitt. 4. 2 Standard Deviations of Turbulent Fluctuations and Stability Dependence The measured standard deviations for horizontal and vertical t— I 0 0' X. I 3 3. w tf J PQ 4^ < i—l H • i-f rt 4J CO O -e~ o ■n b en o 84 \ velocity, and temperature and humidity fluctuations are given in Table 1. Values of the ratios a /u , a /u , a /T and CT /q are u * w * 0 * q > given in Table 3 for stability results and plotted versus -z/L in figure 10. Figure 10 also compares present results for this work with other current results. For each run the averaging time is given under "run duration" in Table 1. The variances and covariances were obtained by integration under the spectral and cospectral curves. Integration of the u and w spectra to obtain variances for OWAX data did not include the area under the peak at 0. 1 Hz due to FLIP induced motion. An approximate correction was made by drawing a faired line through the affected region in a similar manner as was 8 11 done by Pond et al (1971) and Leavitt (1973). Any resultant error from this procedure can be expected to be small since the peak at 0. 1 Hz in the w spectrum for MITOS III data was removed by an instantaneous pitch correction of the w signal using Eq. (39) of Section 3. 4. The u and w spectra from SOMA and MITOS I do not show a large peak at 0.1 Hz since a large part of the FLIP motion was removed by the cable suspension system of these two cruises. The u, values for OWAX and MITOS III were obtained from integration of the uw cospectrum corrected for tilt effects using the transformation equations of Section 3. 4. The uw cospectrum for MITOS III was corrected for pitch using Eq. (39) while the OWAX data was corrected for pitch using the- mean angle approximations of >> FIGURE 10 Normalized standard deviations of turbulent fluctuations plotted versus - z/L a. a /u , , a /u , versus - z/L u :': w * b. a JT , , a /q , versus -z/L 9 * q v \ X) c o ft ft + t- 0 ft in X! ft 5 I cr IS w a) O cr cm * b |h c b CD , " ■i r- •—■V Oco r- CO »-s CO r-< ngaard, mi (197 4-> 44 T3 -t-» 4-> r-l rt c n) C V o ~ 2 0 -1 ft h} 2 b*l3* b I 3 b I 3 b I 3 b I 3 o o <> ■I'M I r O oo to **• I cvj to 6 C\J 6 D < >- J> 3 .» 3 m o MM t- 00 ID o o en CO 5 uj o *■ b°"| J o uf" I • Df- o st- CNJ b* I a < I D 3 D 87 Eq. (41). Any residual peak at 0. 1 Hz not removed by the pitch corrections was faired through with a straight line approximation. To obtain the entire covariance from the cospectra, integration was The lowest between .003 performed between f = 0.001 Hz and f = 10 Hz frequency point obtained from cospectral analysis was and 0. 005 Hz, so that it was assumed that the cospectra went to zero at 0.001 Hz for the integration. The additional area obtained using this integration technique amounted to an average of 7% for the uw covariance and 4% for the wy covariances. The u, values for the 2 —2 SOMA and MITOS I runs were calculated from the relation u , = C U since no correct pitch angle was available to obtain pitch corrected _3 uw cospectra. An assumed value of C = 1. 3 x 10 was used in the calculations of u , . This value of C is an average value * D / 52 obtained from the results of Deacon and Webb (1962) who suggest — -3 -3 C = (1.0 + 0.07 U) x 10 (average 1.47 x 10 for SOMA and 53 33 MITOS I cruises), Hasse (1970) ' and Miyake ct al (1970) who give -3 -3 values of C of (1.21 ± 0.24) x 10 and (1. 1 ± 0. 18) x 10 for 54 slightly unstable conditions similar to the SOMA cruises, Smith (1970) 3 8 who obtains a value of (1. 35 ± 0. 34) x 10" , Pond et al (1971) who _3 obtains (1. 5 ± 0„ 26) x 10 for BOMEX results, and Mitsuta and 55 -3 Fujitani (1974) who suggest 1.22 x 10 from Northwest Pacific Ocean and East China Sea data. Also included in the average is the present result from the MITOS III and OWAX cruises of (1. 18 ± 0. 20) 88 -3 x 10 for pitch corrected data. The ratio O /u , for this work is 2. 84 ± 0. 53 . This ratio u * historically has shown considerable scatter when plotted versus z /L and values of CT /u v for neutral stability range from u 1 . 8 obtained by 56 Kaimal et al (1972) to 2. 3 suggested by Monin ai|id Yaglom 27 -2 (1971). Their value is shown at - z/L = 10 in figure 10a. Leavitt (1973) obtained a value of 2. 8 ± 0. 5 for a /u , from u * BOMEX data in the stability range of 0. 1 <- z /L < 1. 0 which is 55 represented by the dashed line in figure 10a. Mitsuta and Fujitani report a value of CT /u , = 3. 30 ± 0. 78 for - z /L =* 0. 2 from their u v work in the Northeastern Pacific and East China Sea for measurements taken from a cruising ship corrected for ship inotion. The predicted shape for the behavior of the ratios o /u , , c w * (7_/T , and a /q versus - z/L is given by the relations 6 * q * 1/3 a /u, = C (- z/L) ' w * w -VT, = CT(-,/«-1/3 (42) -1/3 -a /q = C (- z/L) q * q where C , C and C are constants and u, , T. , and q, are w T q * * * given by Eqs. (5) and (6). Values of the ratio a fxx for the OWAX and MITOS III runs with pitch corrections show considerably less 89 scatter than those ratios calculated using an assumed C . The pitch q corrected values of a /u agree well with the results of Pond et al, 11 57 Leavitt and Monji (1972), are slightly higher than the results of (TO Wyngaard, Cote and Izumi (1971) for Kansas data, and slightly 55 11 lower than the results of Mitsuta and Fujitani. Leavitt estimates C =1.7 although his data show the trend represented by the dashed q and dotted line in figure 10a for 0. 1 < - z/L < 1. 0 . Pond et al from BOMEX data obtain an average value for a /u = 1. 32 ± 0. 0-9 W :': represented by the dark triangle in figure 10a. The dotted line of figure 10a represents a result of C = 2. 2 given by Monji froin data obtained at the Bonneville Salt Flats in Utah. The "Wyngaard et al 56 and Kaimal et al result of C =1.9 from Kansas data is represented w 55 by the unbroken line of figure 10a. Mitsuta. and Fujitani obtain a value of a /u , = 1.68 ±0.2 for -z/L,— 0.2 . The ratios a /u , and w * u * (T /u show that the large scale velocity field is anisotropic. Spectral results will be given in Sections 4. 5 and 4. 7 illustrating the approach to isotropy for the small scale structure of the velocity field. The ratios - 0" /T and - CT /q , obtained for this work are 6 * q * 58 shown in figure 10b and follow the prediction of Wyngaard et al for C = 0. 95 . Results of Leavitt (dashed line with slope - 1/4) and Phelps and Pond (1971) from BOMEX data shown in figure 10b are higher than their San Diego data and ratios from this work. The ratios O ./q , for the MITOS I and SOMA data are lower than the results for q * 90 the OWAX and MITOS III data. In general for the SOMA and MITOS I cruises the values of U /T are higher than the values of a /a as o ''- q ** 10 was found by Phelps and Pond for BOMEX results. The OWAX and MITOS UI ratios are more nearly equal as was found by Phelps and the Wyngaard Pond for pre -BOMEX (San Diego) data which follows n58 ,. . > et al prediction more closely than the BOMEX data. The high values of a /T^ for the SOMA cruise are not surprising due to the uncer- tainty in the assumed C value, the small sensible heat fluxes measured during the cruise, and the possible effects of non-station - arity at low values of - z/L, . Near z/L. = O^cr /TA versus z/L exhibits a cusp-like behavior which makes the ratio more uncertain and difficult to measure 4. 3 Pitch Corrected Covariances and Error Analysis Covariances determined by the eddy correlation technique are fairly difficult to measure as noted in Section 2. 1. In addition to the errors caused by platform (sensor) motion, the measurements are also sensitive to instrument alignment errors and cospectral distortion at high frequencies due to spatial averaging and sensor separation. The covariances obtained for the MITOS III and OWAX cruises were corrected for platform motion errors due to pitch using simultaneous pitch angle measurements of a vertical gyro mounted at a known angle with respect to the velocity sensors (sonic anemometer). Spatial averaging of the sonic anemometer occurs over a path length of 20 cm 91 so that the smallest wavelength resolved is 1.26 m . Effects of this spatial averaging on the velocity spectra and cospectra occur at f z/U values of 10 for MITOS III and Z. 8 for OWAX (discussed in Section 4. 5a. Distortion of the scalar flux cospectra at high frequen- cies due to sensor separation is more pronounced since the sonic anemometer and temperature /humidity sensory were separated by — 50 cm , reducing the high frequency cut-off to f z/U values of ^1.0 and 4 for the two cruises. No correction for spatial resolu- tion or sensor separation was made since contributions to the covariances above f z/U = 1 are small. The resultant error in the co variances is less than 5% for the OWAX cruise and negligible for the MITOS III cruise. The sonic anemometer used to measure horizontal and vertical velocity during the OWAX cruise had a misalignment of 1.1° in the vertical sensing path which induced u- contamination in the measured vertical velocity. The covariances which include vertical velocity have been corrected to account for this misalignment represented by (p in the equations of Section 3. 4. The measured pitch angle spectra of the vertical gyro for MITOS III and OWAX is shown in figure 1 1 as log f <& (f) plotted versus 6 ii i i i i i i 1 n t i i-i — i — i linn i — i — i m i rr i — r — r i O ro i O d)ti ( S99j5ap)(j) c£)j 94 spectrum also exhibits a peak at 0. 01 Hz and in general has a higher spectral level than the OWAX spectrum for f < 0. 04 Hz . Mean pitch angles and values of a for the MIT OS III and OWAX cruises are presented in Table 4 . Also given in Table 4 are the corrected vertical velocities (w) , the uncorrected a measured and nd corrected uw covariances with confidence limits, and values of -R (f) = <£ / uw uw 1 /2 ($ $ ) in the frequency band 0. 01 < f <0. 1 calculated for each uu ww pitch corrected run. A comparison is also made with two other methods of estimating the pitch angle in lieu of actually measuring the angle. Table 4 gives uncorrected and corrected scalar flux covar- iances with confidence limits. The mean pitch angle from the MITOS III cruise shows a much greater variation than those from all the OWAX runs, with (X > CO .

f uw > 0. 1 . Leavitt obtains a value of R = -0. 35 for his 30 m uw 97 data in the same frequency interval using a pitch angle correction calculated from the relation ' - . -i / *» \

f normalized velocity spectra presented in Section 4. 5a, the spectra ire normalized with the expression for the dimensionle s kinetic energy lissipation $ . If the normalized correlation coefficient is determined ~ — 2/3 1/Z >y the relation r = uw $,. / (

) ' (see Appendix .1), the uw € uu WW verage value of -r = 0. 25 ±0. 06 for the pitch corrected data using uw r 6 &2/3 = «E> - z/L)2/3 (Eq. (24)). For 2 /3 = (1 + 0.5 \z/l,\Z/.3) , the 1 m 2 iverage value of -r = 0. 30 ±-0. 06 . The value of -r = 0. 25 for uw uw 59 P , agrees with the value obtained by Miyake et al (1970), (0. 25) 1 « md the standard deviation of the result is reduced. The overall values of r „ (0. 48 ± 0. 04) for the OWAX and MITOS W0 II data corrected for pitch are higher than those obtained from SOMA and vIITOS I runs (0. 16 ±0. 11) . The pitch correction to the w6 and wq :ospectra is small compared to that for the uw cospectra, so that the :rend in the r _ values is probably real. Phelps and Pond also w8 obtained higher values of r „ for pre-BOMEX (San Diego) data than w8 :hose obtained from the BOMEX data. The average value of r from all the cruises for this work is 6 wq ).43 ± 0. 11 . There is a slight trend for the values of r for OWAX b wq md MITOS in to be higher than the SOMA and MITOS I values, but is lot pronounced as the trend in the r „ values. The overall correlation W 0 coefficient r given by Phelps and Pond for BOMEX data (0. 3 3) is wq ° ' r 101 comparable to the average value of r for the MITOS I and SOMA v/q cruises (r =0.36). . wq The r values for each run are lower than the corresponding r values with the exception of OWAX 4 which shows the opposite behavior. It is difficult to notice any real trends in the r and r u9 uq values and the u0 and uq covariances since they were not determined for the SOMA cruise. The anamolous high value of ~ r = 0. 78 for uq run MITOS 1-1, which also has the highest wq and uq values may be due to drift or misalignment of the x-wire in the mean flow since the r value unaffected by pitch is comparable to that obtained from Qq MITOS 1-7. The value of uq for MITOS 1-1 is comparable to values of uq obtained by Phelps and Pond during BOMEX. Results obtained for r for this work agree with those obtained 6q by Phelps and Pond ° from pre-BOMEX (r ~ 0. 8) and BOMEX D SI (r^ = 0. 5) temperature aiid humidity data. Lower values of r 8 q r 6q were obtained for the SOMA and MITOS I cruises (0. 38 ± 0. 09) than were obtained for the MITOS III and OWAX cruises (0. 73 ± 0. 13). The correlation coefficients which include the scalar s can also be normalized in a similar manner as was done for the r correlation uw coefficient. The normalization for the r and r correlation wy uy coefficient is (<£> ) <£ where y is equal to 9 or q , and the H C - 1 /3 normalization for the r correlation is 3> $ (sec Appendix 1). The normalized correlation coefficients are given in Table 5. TABLE 5 - Normalized Correlation Coefficients 102 1 r . w9 r \vq ru6 r uq SOMA 0. 06 0.20 - . , . , - 0.21 2 0. 05 0.29 - - 0.21 3 0.09 0.27 - 0.2 9 MITOS I 1 0.24 0. 36 0. 19 0.62 0.28 7 0. 18 0. 33 0. 13 0. 33 . 0. 22 MITOS III 2 0. 35 0. 38 0.23 0.2 3 0. 22 OWAX 2 0.25 0.29 0. 14 0. 12 0.26 3 0. 32 0. 33 0. 14 0. 14 0.43 4 0. 35 0. 36 0. 39 0 .29 0. 39 r*-t -*„1/2V/6 xy axay X = u, W 7 = e>q 6q = 1/3 6 q 103 The f; rs

v *Figure 17 shows the MITOS III w spectrum corrected for pitch (<) and uncorrected ( + ) sampled at 3.0 Hz. 1C5 sampling frequencies used to digitize the analog data. The record length for each spectral computation was 512 words /record/channel. Each spectral realization at different sampling frequencies was calibrated in absolute units, 20tb decade averaged, and matched to the lower frequency spectra. Not all tbe points from each spectral realization are shown in order to reduce overlapping points and because the end points of each realization are iiffected by the filter cut-off (Nyguist frequency). 4. 5a Velocity spectra Absolute horizontal velocity spectra for SOMA, MITOS I and MITOS III/OWAX are shown in figures 12, 13, and 14. The vertical velocity spectra from, these cruises are shown in figure 15 - SOMA, figure 16 - MITOS I, figure 17 - MITOS III and figure 18 - OWAX. Only the w- spectrum of MITOS III is shown corrected and uncorrected since an instantaneous pitch correction was employed for this cruise. The averaged u and w spectra are shown in figures 19 and 20 normalized 2 with u4 and plotted versus f . The large peak in the u and w spectra between 0. 05 < f < 0. 2 Hz due in large part to wave induced FLIP motion is more pronounced in the OWAX spectra (z = 350 cm) than in the spectra from SOMA, MITOS I and MITOS III. For both the OWAX and MITOS III cruises the instrument package was rigidly attached to FLIP, while for the SOMA and MITOS I cruises the instrument package was FIGURE 12 SOMA horizontal velocity spectra plotted versus frequency 107 ro CJ O O nn. ( oas/ ujo) qi FIGURE 13 MITOS I horizontal velocity spectra plotted versus frequency 109 CM ¥f + v o o o • o o cm I o ro oo O to TTT-rri — i — t |ii i i i i — r — i |m >. i i — i — i inni i i — r to CM O o o nn. ( 09S/ UJ0)(J) (£J FIGURE 14 MIT OS HI and OWAX horizontal velocity spectra plotted versus frequency j FIGURE 16 MITOS I vertical velocity spectra plotted versus frequency .115 CM o O - O _ o CM I o o to CM O O (_OZS/^D)(>f%l FIGURE 17 MITOS III vertical velocity spectra plotted versus frequency corrected for pitch (0 ) and uncorrected ( + ) 117 CM O o o- o N X o I o ro O <4 MM. (209S/2UJ0) d> J- FIGURE 18 OWAX vertical velocity spectra plotted versus frequency 119 WZ.+ 1 , l'+ x+ o o o o him i — i — i 1 ii 1 1 i i — i — i |i 1 1 i i i — i — i 1 n 1 1 i i — i — i — t ■ ro cvj /'V -^'" O o o o o o N X o CM I o ro 0) ro ro Oco MM. (208S/2UJ0) (J) ^J 120 suspended on a cable. This suspension technique did appeal- somewhat successful in reducing the wave induced FLIP motion effects on the velocity spectra. Figure 17 shows pitch corrected and uncorrected w spectra from MITOS III to illustrate that the instantaneous pitch correction does appear to remove the peak at 0. 1 Hz for this data, although only one high uncorrected spectral value at that frequency is shown. The peak at 0. 1 Hz in the velocity spectra may also be due in part to the effects of Waves on the turbulent flow field as suggested by the results of Lai and Shemdin (1971). These investi- gators found that simple mechanically generated water waves had a noticeable effect on the velocity spectra (u,w) and cospectra (uw) at the wave frequency. A maximum percentage increase in a and a of 24% and 9% respectively was found at heights above the water w between 10 and 50 cm . The water waves did not appear to have any affect on the spectra in the inertial subrange. The sonic anemometer horizontal and vertical velocity for the OWAX cruise, and vertical velocity spectra for the MITOS III ■ cruise have not been corrected for spatial averaging and exhibit a fall- off in spectral level at lower frequencies than the x-wire and hot film velocity spectra. With a path length of 20 cm the response of the sonic anemometer should be accurate for f S 10 for MITOS III and fN ^ 2.8 for OWAX velocity data according to the relation FIGURE 19 Average horizontal velocity spectra normalized 2 with u_,, plotted versus normalized frequency (f z/U) • ■ • . 122 CM d± \ X o o o o _ o 1 1 ■ i ! i—i — i — i prm-i — i — r rTTT-n—r i [ii 1 1 1 .-~t — r 1=3 N CVJ •o CO ro ro ro 0(J3 .'■_ . o c\) o o 'o 'o ro 'O ■ nn. 2n/U) ± FIGURE 20 Average vertical velocity spectra normalized 2 with u. plotted versus normalized frequency ' -..'•;.., 124 M o ro (0 o o CM i _ ro i ..■'.:.. O ,*n / (lf%l 125 fz/U = z/Zvtl (45) where z = 1250 cm (AUTOS III) and 350 cm (OWAX), and I = 20 cm. The averaged u and w spectra oi* figures 19 and 20 2 normalized with u are in fair agreement with the Kansas 56 data ot Kaimal et al (1972) represented by the dark line in both figures. In general the spectral values for the SOMA and MITOS I are higher than the OWAX and MITOS III spectra for f > 2 , possibly due to uncertainty in the u. "-values and also due to sonic response for the OWAX spectra. To remove the z/L dependence of the velocity spectra, an 2/3 additional normalizing factor is required, namely $ , where kz <£ = — £ from Eq. (23). The inertia! subrange form of the u spectra given by Eq. (11) may be rewritten as f $ (f ) a. $2/3f-2/3 (46) 2 2/3 € N u;,; (ZttK) For this work an a value of 0. 53 was used based upon direct u dissipation results from MITOS I, MITOS III and OWAX 4 in the 50 concurrent work of McConnell (1974). For an a =0.53 and K = 0. 4 , (46) becomes VuuV = Q>29 f2/3 (4?) 2^ 2/3 ' N u, $ * e FIGURE 21 Average horizontal velocity spectra normalized 2 2/3 with u.,„ and <& (assuming total production €1 = dissipation of kinetic energy) plotted versus normalized frequency 127 O O o CO i o ro i 3 » / , nn FIGURE 22 Average vertical velocity spectra normalized with 2 2/3 u„,, and $ plotted versus normalized frequency ■ '; ■ l: ■ -■ ' 3 ^ , ,MM FIGURE 23 Average horizontal velocity spectra normalized with u and $ (Wyngaard and Cote ) €2 expression for normalized dissipation plotted versus normalized frequency ■ •*'■■■••■!■:.: 131 OJ O O O o OJ 1=3 V, N O O ro ■? *. O «5 •■ ■*>, ■ 2/2 2 FIGURE 24 Average vertical velocity spectra normalized with 2 2/3 u ,, and plotted versus normalized frequency €2 .■■■■-.- Cv! A ~l — I r * x ■■■■'. .-'■ T 'Mil i — i — i 1 1 < ' i : t — ? — i r o o O o o cv) i o 1 3 ro cr> ro O CD ■} — CVJ to III O O O O ■ - M/A. 134 A similar relationship can be obtained for the w spectra by assuming isotropic conditions and making use of the relationship $ = 4/3 $ ww uu in the inertial subrange: f * (f ) N 0.39f" 2. 2/3 "* N 48) Figures 21 and 22 show the f u and \v spectra normalized with t! expression $ = [(1-16 z/L)" -z/L.] from Eq. (24), assuming 1 % dissipation of mechanical energy is balanced by buoyant and mechanical production. This normalization is compared to the results of Leavitt (dark line figures 21 and 22) who obtains from BOMEX data values of 0.28 ±0. 05 and 0. 37 ±0. 07 for the constants in Eqs. (47) and (48). Figures 23 and 24 show the f <3? and spectra normalized with N uu ww 2/3 i 2 /3 the expression $ = (1 + 0. 5 | z/L,| ) from Eq. (27) based on the C2 /37 results of Wyngaard and Cote' who used values of a = 0. 5 and K = 0. 3 5 to obtain their normalized velocity curves with values of the constants for Eqs. (47) and (48) of 0.296 and 0.394. Constants obtained from this work for Eq. (47) are 0.29 ±0.06 for $2/3 and 0. 23 ± 0. 06 for and 0. 40 ± 0.09 Cl f2 and 0. 32 ± 0. 09 for Eq. (48). A more sensitive test of the two expressions for $ will be discussed in Section 4. 6. A test of the validity of the inertial subrange relationship $„ = 4/3 * „ w]l \v\V UU issumes local isotropy is shown in figure 25. The average ratio FIGURE 2 5 Spectra ratio / <3> plotted versus WW uu normalized frequency ':-.'• .?•'••••■ ."•/.?-.•■•...'.• .'..■• •;'■••;":. .;;;.-/;..;-• 136 CVJ X X X X X X X ^x ■+ + + •+ + ++ A >&*• ^ + X + *^> + ■^ A-+ + «. -+AA + A <^X + "v X V -a o o o f$* '■■;■ x^ X 13 N 4- o o o 6 LO b o CvJ I ro "*> o LO O o o b nn_ mm_ 137 $ / for each cruise is plotted versus f . The OWAX and ww uu N MITOS III spectra have approximately the required ratio while the MITOS I data is higher and the SOMA data is lower than the required ratio. The high and low ratio values of the MITOS I and SOMA data may in part be due to x-wire drift experienced during the two cruises and discussed in Section 3. 2c, due to salt contamination on the probes. Both MITOS I x-wire runs experienced 30% drift in the velocity calibrations but were matched with cup anemometer results which agreed well with the mean of the before and after run calibrations. The SOMA x-wires were calibrated only before each run so that the absolute drift is unknown and only run 1 was matched with a cup anemometer. For this reason the averaged normalized SOMA velocity spectra are probably inordinately high and are not included in the estimates of the constants in Eq. (47). 4. 5b Temperature and humidity spectra Absolute temperature spectra for SOMA, MITOS I, and MITOS III /OWAX are shown in figures 26, 27 and 28; absolute humidity spectra for the cruises are shown in figures 29, 30, and 31. Micro- bead thermistors were used to measure temperature fluctuations for the SOMA cruise and for OWAX runs 2 and 3. The temperature spectra of MITOS I, MITOS III and OWAX 4 were obtained from cold wire temperature data. Humidity was measured with the Lyman-Alpha humidiometer for all cruises. FIGURE 26 SOMA temperature spectra plotted versus frequency •: •...-.. • ■ . . - . '•■•.■ ■••.v.-:*.* •■ .>: 139 CJ v v V J? 4T S7= ?? V v> x^:/ + ^.X^xW + + + + ft # 3; x ^&x XT vXX 5? Xv X X X + o o nrm — i — t pun i — i — i rrrmn — i — i — : — p"i ' ' ' ' . ' r N X O i O i CO I i i o o (3=o)°°* FIGURE 27 MITOS I temperature spectra plotted versus frequency '■■■■.■■■■•"■ -'■■•■•. ->■■. Ml 89 142 '•'.; ■ ..-■ .1 FIGURE 28 MIT OS III and OWAX temperature spectra plotted versus frequency (in i t i — r — i pi i i i i — i — i |i it i i i — i — i — — in 1 1 i i i — r r I ro i O i o o (30o)eV FIGURE 29 SOMA humidity spectra plotted versus frequency ■ . I .^ J i i ; i ¥% V t ^ X + ■^ + X + X + |M i I i ii — 1 pi i ii i i — i pi ii i i i — i |in ii i i — r OJ O o o o N o OJ I o ro CM O ■ ! OJ J* 4+ ^ 4^ SZ O # + 5* + ^ + ^ + ^ + v O O O X o CM i o ro CM C\J <3- O to • "mi iii — 111 ii ) i -1 — i — : — 1 1 1 ii i i i — r — ii r 1 1 i i i — -i — > — oj ro \t o 'o 'o 'o 'o bb. (£UJ0/UJ6*/)U) <£>* FIGURE 31 MIT OS III and OWAX humidity spectra plotted versus frequency ■ . ; ' ' . ■ - CM &*0 V ■ X ^ + ^Q X "* + D D X ^ + □ D X ^ +□ o o o o o C\J 'o IM X 10 c\j ro O^o 1 Hz since above that frequency the spectra roll-off due to thermistor response. The humidity spectra from all cruises are. similar and appear -2 /3 to follow a f behavior for f >0. 8 Hz and do not exhibit any high frequency peak. The MITOS III humidity spectra obtained at 12 50 cm exhibit the most pronounced inertial subrange for f > 0. 2 Hz . Differences between temperature and humidity spectra and between individual runs for the temperature spectra are shown in figures 32 and 33 which present average temperature and humidity 2 2 spectra normalized with T and q plotted versus z/L. The -2/3 humidity spectra collapse quite well and exhibit a f behavior for f > 0. 3 . The temperature spectra do not collapse and only the M ITOS I temperature data exhibit a -2/3 behavior for f > 2 . ture spectra of MITOS III and OWAX appear to follow a -1/4 sl< FIGURE 32 Average temperature spectra normalized with 2 T.,. plotted versus normalized frequency . ' w . ■ ■ . I j,*l / U) 8% i FIGURE 33 Average humidity spectra normalized with q plotted versus normalized frequency :'.;'■ : I CM -1 ^ Q* ^ X ^ X ^+ X + ^ +^a X +1 X 5 A x + X X nrm — i — i pi ittt- t— i 1 in i i' i l "i ' iirrni t o o - o CM i N O rO 'o<4 o CM i „ ro i O b/[i)%l >ver 2 1/2 decades for fN>0.5. The >ression for the temperature fed humidity spectra in the inertial subrange given by Eq. (12) can be rewritten as fVf) ^y . .•.!« -2/3 -ft~ - — fT/3 Vc £N <"" y (2tt k) where y - T or q, $ is the dimensionless scalar production given by Eq. (19), $ the scalar subrange constant, and K = 0.4 .• The dimensionless scalar production of temperature and humidity variance las been assumed equal and in balance with the dimensionless scalar dissipation given by Eqs. (30) and (33) for temperature and humidity. This assumption may not be valid as will be discussed in Section 4. 7. Figures 34 and 3 5 show the averaged temperature and humidity spectra normalized as in Eq. (49) and plotted versus f . Also shown in these figures are the temperature and humidity spectra of Phelps and Pond and Leavitt for BOMEX data, Phelps and Pond for pre-BOMEX (San Diego) data, and Wyngaard ' and Kaimal for Kansas temperature data, normalized in a similar manner. Data from -1/2 -1/3 this work has been normalized with <±> = (1-16 z/L) and

plotted versus normalized frequency :V ;.•'.■'.' • •' . -• 157 CM 00 rt o l-H O") - bt W X W co W """ 2 *2 13 0g|» W PL, & T3 * ■ i% •r< (X £< to J PL, Ph £ • I1 .' •i i' i i i r ■! — r o 'fin i 'i i "t fm i'ri -i — r I IT I I'l 'I I O o o CM i o ro i O o o o o ISI I o CM CD l-O ro ^ 'o «? O £ / l$%-±/U)e%* FIGURE 35 Average humidity spectra normalized with 2 q, , (dimensicmless humidity gradient) $ -1/3 plotted versus normalized frequency 159 CM v . * -x o ^ ^,+X X W w W "~w ^ fl -o O o o m & Oi Jj 01 10 i> H i— I Bl 1) O J ft Oh • l . I l O o o . o 1=5 rsi . O cvj i O fO i O<0 f I I I I I II 1 p ! I ■ I I 1 1 |I1 I I I 1 I 1 -_|ll I ) I I I 1 O - cvj" ' -fo O o 'o 'o 'o 160 58 Wyngaard Kansas data, represented by the solid line in figure 34, if normalized with the expressions in this work and K = 0.4 would be approximately 3% lower (based on - z/L= 0. 2) than shown. The temperature and humidity spectral data for BOMEX and pre-BOMEX cruises shown in figure 34 and 35 was obtained by fai -nip, a mean line through Phelps and Pond's spectral results. Since their results were normalized with a and a , the normalization of figure '■ I 2 2 was calculated based on average a /T;1. = 4.23 for pre-BOMEX and 6.63 for BOMEX (this includes correction for K in their definition — 2 2 of T\,, = w0/Ku.J, a /q, of 4. 84 for pre-BOMEX and 5.25 for q * * BOMEX, and average - z /L values of 0. 165 (pre-BOMEX) and 0. 195 2 2 -1/3 (BOMEX) to calculate the values of T\„ , qo, , $ and $ . The * H C -1/3 expressions for $ and $ used to normalize the Phelps and Pond data were the same as those used by Leavitt. The Phelps and Pond and Leavitt BOMEX temperature and humidity spectra shown in figures 34 and 35 agree for f >0.05 and are higher than San Diego data of Phelps and Pond and spectra from this work. The normalized humidity spectra of Phelps and Pond differ by 10% due to the different conversion factors. This difference is greater by as much as 25% for f > 0. 2 , probably caused by low pass filtering of the San Diego data at a lower frequency than the BOMEX data as noted by Phelps and Pond. The 10% difference in the normal i/ average humidity spectra of Phelps and Pond may be due to seal' 161 in the Phelps and Pond spectra but appears to be real when compared to the humidity spectra of this work. The general trend in the normalized temperature spectra is for the warmer more humid BOM.EX and MIT OS I data to be higher than the Kansas land (dry) spectra and the less humid San E'icgo spectra. \ The temperature spectra from MITOS III and OWAX 4 do not follow the -2/3 predicted f behavior for f > 10 as shown by the Kansas data. The MITOS I temperature spectra have the same shape as the; BOMEX -2/3 data and follow the predicted f behavior for f > 10 . The San N N Diego thermistor data of Phelps and Pond does not extend beyond f , — 8 and has the same shape as the thermistor spectra of the SOMA. N r and OWAX 2 and 3 runs. The Phelps and Pond data do not extend beyond f =10 and Leavitt' s average temperature spectra shows scatter and response limitations above £ = 10, so that any comparison of spectra for f ' > 10 is tenuous. The normalized temperature spectra of figure 34 are higher in spectral level than the corresponding normalized humidity spectra of figure 3 5 for f > 1 . No attempt was made to average all the tempera- ture and humidity spectra for comparison of the two on one plot due to the large spread of the individual spectra from different cruises. Comparison of the constant /? and /3 which can be obtained from Eq. (49) will be made in Section 4.7a. 162 4. 6 Cospectra Results of cospectral analysis are presented in this sectio l, Cospectra from the four cruises are presented in a manner sin Liar to the presentation of power spectra, with averages and plot symbols Remaining the same unless otherwise noted. Two realizations Eor each cospectral computation were made at the two lowest sampling frequen- cies shown in Table 6 for each run. Since the correlations between the variables being compared in the cospectral analysis are less than unity, cospectral estimates will have larger uncertainties than spectral estimates, at the same frequency, particularly for low frequency estimates. Uncertainties in the cospectral levels at lower frequencies have been minimized by the long averaging periods. The number of estimates of the lowest frequency cospectral points at f = 0. 004 Hz is between 170 for the OWAX 3 run and 32 for the MITOS III data. The cospectra from the MITOS III and OWAX cruises have b< corrected for internal misalignment of the sonic anemometer (OWAX only), instrument pitch, and wave induced FLIP motion using the procedures discussed in Section 4. 3. The uncorrected wy cospecti from the MITOS I and SOMA cruises are also presented, since scalar flux cospectra are less sensitive to motion effects than the uw cospectra. The momentum flux cospectra from MITOS I and SOMA are not prr icnted since no pitch angle was available to obtain pi 163 uw cospectra, and the (uw) cospectral estimates are sensitive to drift of the x-wires experienced during the two cruises. 4. 6a Cospectr£i of momentum (uw) Absolute (uw) cospectra from M1TOS III and OWAX plotted versus frequency (f) are shown in figure 36. In the frequency range 0. 01 < f < 0. 1 Hz used to determine the value of the spectral correlation coefficient R (f) , the spectra exhibit a broad, fairly uw constant peak. No cospectral estimates were made below 0.001 Hz . Cospectra of momentum flux presented by Leavitt and extending to 0. 0001 Hz exhibited considerable scatter and negative values in the frequency interval 0. 0001 < f < 0. 001 Hz , so that there are only small (< 5%) contributions to the uw covariances below 0. 001 Hz . The averaged uw cospectrum of OWAX and the MITOS III 2 cospectrum normalized with u. and plotted versus log f are shown / 61 in figure 37. Wyngaard and Cote predict an inertial subrange behavior for the uw cospectra given by the expression iV™ V . „ Q(z/L)f-4/3 (50) £ uw N where the function G (z/L) = 1,0 determined empirically from Kansas 56 data by Kaimal et al for -2 £ z/L ^ 0 , with a predicted value of the constant a. =0. 048 , The cospectral curve predicted by Wyngaard uv/ land Cote is shown by the dark line in figure 37 •where the divergence FIGURE 36 MITOS III and OWAX momentum flux (uw) cospectra (corrected for pitch) plotted versxis frequency *„ +-^ + 4- + V ■+ V I %* 2 XS> + cF 9- d * _ + D □ V> X o o o CM i o M -OX ro ro i ii ii i i i — i f'm ,|"1 ' — i rrrrrrT-i — i fin i r l i — r O & ro CM o o O Mn (209S/_,UJ0) (J) qp J- FIGURE 37 Average uw cospectra normalized with 2 u0, plotted versus normalized frequency (comparison with other results) • . 167 O i O ro i O N TTT-TT — I 1 -T o TTTT n — i — i r cvl O ID ro i O ^ TTTT-n — i — i r ro Mn 2*n / (i)M,, 0. 2 , but are lower in cospectra]. level N N ^ than the Kaimal et al~ or Pond et al cospectra. The value -of a - 0. 01 ± 0. 002 for this data also illustrates the lower cospectral uw levels. Lower cospectral levels for f >0.2 for the MITOS III and N OWAX data cannot be completely explained by spatial averaging errors. -4/3 The two cospectra collapse on one another and exhibit a f behavior over nearly a. decade in the range 0.2 i © M® o 6 o ro 6 o CvJ T O 6 o o • o 2-n/MV o L O u o o CVJ i - o 13 \ N ro i ^ _ O -<-> ■ +-> • rH > n) CD ro • T * O <£> o I 171 the sonic anemometers used during the OWAX and MITOS III cruises, noise in a single channel may have contributed to the faster roll-off in the cospectra. The behavior of the uw cospectra at higher frequencies (f > 0. 2) may be due to effects other than spatial averaging and high frequency noise. Both normalized cospectra from the MITOS III and OWAX compare with one another and have the same shape as the uw 56 cospectra obtained by Kaimal et al . The spectra appear to be shifted to lower frequencies, suggesting that production of kinetic etiergy may occur at larger scales over the ocean than over land under certain conditions. A correction was applied to the OWAX cospectra for the internal misalignment of the vertical sensing path, however, this distortion may have contributed to lower cospectral levels for f > 1. 0 The normalized uw cospectra are shown plotted linearly versus log f in figure 38 and compared with Leavitt's averaged uw cospectrum (circles). Leavitt obtained a value of a = 0.07 ± uw 0. 02 from the 8 in normalized cospectra. The cospectra from this work are lower than Leavitt's data for f >0.2 and show evidence of N possible high frequency noise contamination with positive high frequency cospectral values for the MITOS III data above f =0.7. The low frequency cospectral levels (f <0.01) are, in general, slightly higher than results of Leavitt, probably due to the difference in pitch correction procedure. 172 4. 6b Cospectra of heat and water vapor flux (w9 , wq) w9 Cospectra Dimensional w0 cospectra are shown in figure 39 - SOMA, 40 - MITOS I, and 41 - MITOS in and OWAX. The SOMA w9 cospectra do not exhibit similar shapes; possible reasons for this behavior have been proposed earlier and include the low w9 covariance values indicating near neutral conditions and suggesting effects of non- stationarity, uncertainties in the w and 9 calibrations, and lack of pitch corrections. The SOMA data also have the shortest averaging time and only extend to a low frequency cut-off of 0. 015 Hz so that uncertainties in the calculation of cospectral levels are equivalent to the other cruise data. The MITOS I w0 cospectra have a peak at £ =- 0.5 Hz and exhibit a shape similar to the shape of the BOMEX w9 cospectra shown in figures 42 and 43. The dimensional w9 cospectra of MITOS III and OWAX corrected for pitch are different than the MITOS I w9 cospectra and exhibit a broad peak in the frequency interval 0. 01 _ O O N CVJ I O ro en ro O CD in ii I — i — i in 1 1 i i — i — i nrmn — i — i irrrrri — i — I O _ cvJ ro O o 'o 'o 'o 0M (0 9S / LU0-0o) (J) (J) J- 179 Section 4. 2. For subsequent cospectral plots, those assumed points will also be circled. Figures 42 and 43 show averaged wQ cospectra from all the cruises normalized with u,,9.„ the negative heat flux (-- -wQ ) plotted logarithiTiically and linearly vs log f . Differences between the MITOS I and MITOS III and OWAX data include an apparent shift of the MITOS I data to higher f values than the MITOS III and OWAX cospectra and a narrower peak in the MITOS I cospectra and lower cospectral levels for f , < 0. 05 . The averaged SOMA data also exhibit a peak at £__•— 0.03 , probably not real since the cospectra were not corrected for pitch effects which are most pronounced for low frequen- cies. The peak in the MITOS I data, is probably real and is comparable Q to the BOMEX results' of Pond et al shown in figure 42 (envelope 11 shown by hatched lines) and the results of Leavitt's averaged wG normalized cospectra shown in figure 43 (circles). An estimated Q average of Pond's et al pre- BOMEX (San Diego) results for w9 are also shown in figure 42 and agree well with the w9 cospectra of MITOS in and OWAX The prediction of Wyngaard and Cote for inertial sub- range w9 cospectra behavior, using arguments similar to those used to obtain Eq. (50) for the uw cospectra, is written as N w8l N' __ . ,_ ., -4/3 a H (z/L,)i _ (bl) u , 9 , w9 w N FIGURE 42 Average w9 cospectra normalized with U.T plotted versus normalized frequency (comparison with other results) ?" . •- ' -._ .. . v-i ' ■ ' J31 _- -=- yr vi i i i — i — i r t~\ — i — i r o CVJ i in i — i — i r O o o c\l 'o ro i la N CD IO ro r < O + rv* + ^ # + A * v ' xx » X X X Q © • X o est ±'n/(i)e%i > a CD -3 1 ' i ■ 1 r o O O O o ro CM — o — O o o o o 1 o o o o CVJ i o N to b Is- ro b(D '■-• ■' ■- :"< '•• 'v',V^-'- 184 where H (z/L) = 1. 0 for -2 £ z/L £ 0 , and the constant a = 0. 14 w \v 6 56 from, results of Kaimal et al. The v/6 cospectra curve suggested by 57 Kaimal et al is shown (dark line) in figure 42, with the divergence in the predicted curve for f < 2 representing the variation of low frequency shapes for different unstable cotiditions; the z/L = 0 and the upper line is for z/L = -2. lower line is for -4/3 The cospectra of MITOS I exhibit a f behavior for N f > 2 , with a = 0. 29 ± 0. 04 , larger than the cc ^ of Kaimal et N w9 w9 56 11 al by a factor of 2 but comparable to Leavilt's result of a - \v8 0. 30 ± 0.08 i The low frequency cospectral points of the MITOS I data for 0.012 < f < 0.03 are lower than those of Leavitt since no pitch correction was applied to the MITOS I data. This difference in the cospectra may also be due to uncertainties in the low frequency cospectral estimates of spectra from this -work and Leavitt' s cospectra. The MITOS III and OWAX pitch corrected w8 cospectra 56 agree well with predicted curve of Kaimal et al for Kansas data and Q the San Diego results of Pond et al, except at higher frequencies, where there is evidence of spatial averaging effects and possible high frequency noise effects above f = 1.3 for the MITOS III data, and above ■ N . v .•"■.• ....••■■' ■ ■ Lr = 0. 3 for the OWAX data. Contributions to the w6 covariance are N not greatly affected by the falloff , illustrated by plotting the normalized cospectra linearly vs log f in figure 43. N 185 The MITOS III value of a n = 0. 06 ± 0. 02 also indicates \v6 that the high frequency cospectral levels are low when compared to the 56 results of Kaimal et al. The w9 cospectral levels are higher than the uw cospectra for f > 0. 2 , and lower than the uw cospectral levels for f < 0. 2 . This is particularly true for the MITOS I w9 cospectra when compared to the predicted uw cospectra of Kaimal 56 et al and the MITOS III and OWAX cospectra. Assuming a = 0. 05 . uw the vertical transport of heat is 6 times more efficient than momentum for MITOS I and only slightly more efficient for the MITOS III data for smaller eddies (f > 1) . The difference in cospectral shapes between the MITOS I w9 cospectra and the predicted and calculated uw cospectra implies that the vertical transport of heat for MITOS I conditions is much less efficient than the transport of momentum for larger eddies (f <1. 0) . The difference in the MITOS III and OWAX w9 cospectra and uw cospectra at low frequencies is not as pronounced as the MITOS I w6 cospectra. wq Cospectra Cospectra of water vapor flux (wq) in absolute units for the four cruises are shown in figures 44-SOMA, 45-MITOS I, and 46- MITOS III and OWAX. The wq cospectra from all the cruises have similar shapes and exhibit a broad peak over the frequency range 0. 01 < f < 0. 3 Hz , the same interval as the peak in the MITOS III and OWAX w3 cospectra, and broader than the peak of the uw FIGURE 44 SOMA water vapor flux (wq) cospectra plotted versus frequency -•:• :• • - 187 bw (09S-2LU0/LU67y)(^) ^ J FIGURE 45 MITOS I wq cospectra plotted versus frequency 189 TLv -Irs* + ^ + * -feZ? v "W*l 'v'" + + ^ + ^ + o o o o x I L O N o ro Si" ro Mill I — I 1 |ll 11 I 1 — I 1 |TT1 1 1 '1 — I 1 |TT n 11"! — i q _ cvj ro O O 'o 'o 'o st bM. (09S- UJ0/UJ5^)(J) gpj FIGURE 46 MIT OS III and OWAX wq cospectra plotted versus frequency (corrected for pitch) i * 19 J ^X JF. t X^ + D □ sfx^J-rp XyXv% X ^ X ^ ■fe + + I* V Tb+° XXS + ^ D © Mill 1.1 1 1 I I II 1 I I 1 [MM I- 1 — r~ 1 ~ 1T1 Mill 1 _ Q — ' CVJ ■•''' "'■'•■•• fO o o xo xo '( o o N o C%J o ro oo ro O S; "• '*'■'" ' ■ . - - ' * *-''■' '■ (oas-2iuo/uj5t/)("i)bMc|)i 192 cospectra. There is evidence of wave induced FLIP motion in the wq cospcctra, with low cospectral points occurring at £ =" 0. 1 Hz (corrected for prior to integration). The expression for the inertial subrange form of the normalized wq cospectrum derived using the same procedures as were done for the uw and w8 cospectra is written as '^W „ „ M (Z/L) £ -4/3 Uo-Cl... wq w N • v ' where it is assumed the function M(z/L) — H(z/L) =" 1 for unstable w w conditions, and a is the cospectraTsubranee constant. This wq expression was also used by Leavitt for presentation of normalized wq cospectral results. Normalized wq cospectra from all the cruises are shown in figures 47 and 48 plotted as log f <& (f) versus lojz f and r * wq\ t> N linearly versus log f ; the negative sign in the normalized cospectra results from the definition of q , so that u q = - wq , the negative water vapor flux. The normalized wq cospectra collapse with the exception of the high frequency end of the OWAX wq cospectrum. Reasons for this behavior of the OWAX cospectrum have been proposed in the previous section. It should be noted that the high frequency end of the MITOS III ^ind MITOS I cospectra are similar, indicating that only the OWAX cospectra are affected by high frequency noise or sensor separation errors. The subrange constant determined from the data FIGURE 47 Average wq cospectra tiormalized with u.q plotted versus normalized frequency (comparison with other resists) • ■■•.-:' r. • ■■" 194 M : O h ii i i i — i 1 O - I' ft l1! I1 "1 — T r TTTTT"-T-*1 r~~ T" I ro i N CJ ro _ O lO ro T * O CD -. o *K * bM b n / U) (J) J- FIGURE 48 Average wq cospectra normalized with u q plotted linearly versus normalized frequency (comparison with other results) •: 196 W v ' , rt 0) h4 - r>- CD • 1 ro o CD ' . o I 197 (excluding OWAX) is a = 0.08 ± 0.02 . This value of a is wq wq higher than a = 0. 01 obtained from the MITOS III and OWAX uw uw cospectra, and a = 0. 048 suggested by Kaimal et al. Leavitt uw obtains a value of a = 0. 11 ± 0.02 , higher but not significantly different from the or for this work. Leavitt1 s wq cospectra wq x also exhibit a sharp fall-off at f ^ 1 for 8 m data so that the values N of a may be slightly underestimated, but are much lower than the wq a values for MITOS I (0. 29) and BOMEX (0. 30). wb 8 The wq cospectra of Pond et al for BOMEX and San Diego data are shown in figure 47; Leavitt' s average wq cospectrum from BOMEX results is shown in figure 48 (circles). No attempt was made 8 to average the BOMEX results presented by Pond et al, and the cospectra are represented by the envelope of the two unbroken curves in figure 47. The pre- BOMEX results are approximated by the dashed curve of figure 47. All the normalized wq cospectra agree, with the exception of the OWAX cospectra for f >0. 3 . All the cospectra may be somewhat underestimated at high frequencies (f > 2) because of noise effects and instrument response. Following the results of Leavitt, the cospectral constants ■ a and ex are related to the spectral constants B and B by the w6 wq 6 q equation ^9 r / I2 (53) — - =- [a /a J ^J-> B w9 wq q 193 if it assumed that II(z/L) = M(z/L) and $ = <£> . Using the values H E from the MITOS I results, a /a = 3.6, implies ft ^ 13 ft . w9 wq 9 ; q Leavitt's result for a A /a =2.7 implies that ft =7.3/3 . The wB wq ^0 ' q high frequency fall- off s of the w9 and wq cospectrii make this relationship between ft and ft somewhat uncertain. A more 6 q \ sensitive test of the relationship between the scalar spectral constants will be made in Section 4. 7. The w0 and wq normalized cospectra are not signifi- cantly different with the exception of the MITOS I cospectra. The MITOS I data suggest that under certain conditions heat is transported vertically more efficiently than water vapor at smaller scales, and less efficiently than water vapor at larger scales. The crossover point at f — 0. 1 corresponds to a scale size of 42 meters using an average height of 42 meters for the MITOS I cruise. The a values indicate that the vertical transport of wq water vapor is relatively more efficient than the transport of momentum for smaller scales (f > 0.2) , although the difference is not as pronounced as the vertical transport of heat and momentum. If the high frequency behavior (0. 2 < f < 2. 0) of the OWAX w8 and wq cospectra is real, it suggests that the production of temperature and humidity variance occurs at larger scales for colder, less humid conditions, than for the warm humid conditions of MITOS I and BOMEX. 199 4.6c Cospectra of horizontal heat and water vapor flux (ue , uq) The dimensional u6 cospectra from the MITOS I and MITOS III and OWAX cruises are shown in figures 49 and 50. Corresponding diinensional uq cospectra are shown in figures 51 and 52. The MITOS HI and OWAX u9 cospectra and the uq cospectra from all runs exhibit a broad peak in the frequency interval 0. 01 < f < 0. 1 Hz and have similar shapes. The MITOS I u8 cospectra have a different shape than the other cospectra and exhibit a peak in the frequency interval 0. 1 < f < 0. 4 Hz for the MITOS I- 1 run, and between 0.2 207 O to 1 1 I I I I I r~ 1 1 1 I II I "1 J— — II I I II 'I — I — ~\ p I'M I .1 "T"T~ 6 — cvi ro O O 'o 'o 'o • ■ i ■ ■ ■ .■■• bn (08S- WO/wM)(J) ^ j_ /6l Wyngaard and Cote is given by the expression fN$u9(fN) , -3/2 = a„0H.(z/L)f„ (54) u ,9 , u6 u N where H (z/L) = 1 for -2 Sz/L^O, and a „ is t u u9 'ie cospectral 56 subrange constant. Kaimal et al suggest a value of a. = 0. 035 . u9 The -3/2 cospectral slope is not as well defined for the u9 cospectra as for the w9 cospectra. Wyngaard and Cote predict a slope of -3 for the inertial subrange of the u9 cospectra from simi- larity arguments. A slope of -3/2 appears to fit the u9 cospectral behavior at high frequencies of the three cruises and is used to 56 calculate the a values for comparison with Kaimal et al results. u9 The MITOS I normalized cospectrum exhibits higher cospectral levels for f T > 0. 2 than the MITOS III and OWAX cospectra, and lower cospectral levels than the other two cospectra for f < 0. 03 . The cospectra have different subrange levels, also shown by the subrange constants for each cruise: a „ = 0. 08 (MITOS I), a „ = 0. 04 (MITOS III), u9 u9 and oc _ = 0.012, with uncertainties of ~ 20% in the estimates. The u9 differences may in part be due to spatial averaging effects and high frequency noise, however, the differences amounting to factors of 2 , extend over nearly half a decade between 0. 3 j FIGURE 54 Average uq cospectra normalized with u ,, q plotted versus normalized frequency (comparison with other results) . . 212 O CM i o ■nil i — i — i — r 1 1 1 t i i ■ ■ 1 — i — t rrrm — i — r ro i O 13 N en io ro * * 'o 0. 04 and are higher than the MITOS I data for f > 0. 6 . The indicated value of the cospectral constant, for the Phelps and Pond data is 56 0. 1 , most pronounced for the MITOS I cruise which also has higher uq cospectral levels than the u6 cospectra for f <0. 1 corresponding to a scale of 50 meters for z = 5 meters. This suggests that horizontal transport of heat is relatively more efficient thai\the horizontal transport of water vapor for small scales. Conversely, for the MITOS I cruise the opposite is true for large scales. The relative efficiency of the horizontal and vertical transport of heat and water vapor can be estimated from the ratios a Id and a la. . The a _/« _ ratios for the three cruises u8 w8 uq wq u9 w8 are 0. 27 (MITOS I), 0. 36 (MITOS III) and 0. 27 (OWAX); the a la ratios are 0. 27 (MITOS I), 0. 1 (MITOS III) and 0.27 uq wq (OWAX). These results suggest that the vertical transport of heat and water vapor is always more efficient than the horizontal transport 56 for small (f >0.2) scales. Kaimal et al suggest this behavior for • ■- , ■ ■ ■ . ' ..'..■ horizontal and vertical heat transport for conditions over land; the reverse is also true for larger scales (f <0.2) . 219 4 . 6 d Cospectra of temperature and humidity (Qq ) The dimensional cospectra of temperature and humidity- are presented in figures 57 - SOMA, 58 - MITOS I, and 59 - MITOS HI and OWAX. The 0q cospectra of SOMA, MITOS III and OWAX have similar shapes. The 0q cospectra of the MITOS I cruise are not so typical and exhibit a narrow peak at the frequency interval 0. 5 < f < 1.0 Hz , similar to the peak in the MITOS I wQ cospectra. The 0 q cospectra have been normalized with T q , consistent with the normalization of the cospectra presented in Sections 4.6a, b, and c. The expression for the normalized 0q cospectra may be written as f ff 1 N 9ql N; __ , ._ ., -5/3 — — — 3 = a H (z/L)f (56) T.„q., 0 q 0q N as suggested from the previous cospectral results. The z /L variation of H is not known and is assumed equal to 1 for unstable conditions 0q as was done for the previous cospectral stability functions. The choice of the -5/3 slope for the 0q cospectral subrange is based on similarity arguments and dimensipnal analysis by Wyngaard (personal communication to C. Friehe and G. Dreyer, 1972). The normalized 6q cospectra are shown plotted as log f$ (f)/T;,q,; versus log f in figure 60, and linearly versus log f in figure 61. The normalized Sq cospectra exhibit differences in the 0 -q relationship at high and FIGURE 57 SOMA temperature -humidity (Gq) cospectra plotted versus frequency i.-':; . ■■:. tr ■:■■'■. ■:.'■•:•■'.■ ■ ■■ ■ «•..■-.. • •' . :" ■ • •; ■ ■ ' ■ ■ ■ - •' • • ' . ■■' - ; : v 221 o o o — N I -r- O i CV! I O 00 00 O CD ' b0, ( LU0/Ol5r/-0o)UDc|)^ FIGURE 58 MITOS I Qq cospectra plotted versus frequency • '■.• • '.- ■•-•.. -s i : •■' lV ' *. ■■'■• *: ' ' ' ' ■ . . ', '"': " : - ' 22 3 v^ ^ / v ■f + + i ! V 2 € \ V + v O o o 1 N 0 X *■■■ "^.-^ tf.~ 1 u o (j) (M O rnr 11 11 — 1 nn r*r~] — ! — r — ;nn rn — 1 — 1 — — -nm-n — 1 — 1 — cj ro *fr 10 'o b 'o 'o 'o b0. ( WO/ wbrJ-0o) (£)J. FIGURE 59 MITOS III and OWAX 0q cospectra plotted versus frequency '. ■:'. < '•'' l v ■ .».. . 225 in J.i — i — r ■V ",p .1. ? >.; -' V"'".-' X_ff LJ D ,++ rf? cP D D n ^ V4 D 3^" 'v\ xv + ^x V # ■^ D ^ + D D rjl a p D D % X ^ D D □ □ 8 D a Xv- + D V + X T'i'i'i r -i — r~"~ r i o o o O X c\J i o CM in ro ro i O } FIGURE 61 Average 9q cospectra normalized with T0,q^ plotted linearly versus normalized frequency ■'...■'- - - - ; - 229 o cvJ O i ...;. ; ■ ■ - ,' '■ ,v^>:,;.;-- b 1/ Cpi 230 low frequencies between the MITOS I cruise and the other cruises, similar to the differences observed in the normalized wG and u9 cospectra. Since the 8q cospectra are presented in this manner, uncertainties in the assumed and calculated u,. values will also affect the cospectral levels, but will not change the shape of the cospectra. The SOMA Gq cospectra may also be affected by temperature calibra- tion errors and uncertainties in the wQ estimates used to calculate T\„ due to x-wire (w) drift and possible non-stationarity effects discussed in Section 4. 2. N The highest normalized cospectral levels are exhibited by the SOMA Gq cospectra reflecting the lower values of the wG covariance. The shape of the SOMA G q cospectrum is similar to the shape of the MITOS III and OWAX cospectra, indicating that the differ- ences in the SOMA wG cospectra shapes is probably due to not correct- ing for pitch effects. The "crossover" point exhibited by the wG and uG cospectra of MITOS I is also well defined for the Qq cospectra of MITOS I at f = 0. 15 (-30-50 meters scale size) . The MITOS III and OWAX cospectra appear to exhibit a slight low frequency peak at f values of 0.023 and 0.015 respectively, corresponding to a scale size of 230 m for the OWAX data and 540 m for the MITOS III data. A slight peak in the 8 m Gq 11 correlation presented by Leavitt is also apparent at. f ~ 0.01 N corresponding to a mean scale size of 530 \r\. 231 TABLE 7 - Cospectral Subrange Constants a a. _ a a a » uw w0 wq u8 uq 9 q MIT OS I - 0.29 0.08 0.08 0.025 0.19 MITOS III 0.01 0.06 0.08 0.04 0.008 0.12 OWAX 0.01 0.03 0.03 0.008 0.008 0.09 Leavitt11 0.07 0.30 0. 11 56 Kaimal et al and 0.048 0.14 - 0.035 Wyngaard and Cote ' ; ' " ' '■:';■ - •'' ' " '•' ' '■'. '■"'' 232 The trend in the normalized \v9 , uQ , wq , and uq normalized cospectra for the colder, less humid runs to show small contributions to the covariance at higher frequencies is also exhibited by the normalized 9q cospectra. Differences in cospectra! level occur for f > 0. 15 , the "crossover" point. A slope of approximately -5/3 is exhibited by all the normalized Qq cospectra in the interval 0.4< £ < 1. 5 . The subrange constants for the last three cruises were N MITOS I, (v = 0.19; MITOS III, cv ="0.12; and OWAX, a 9 q 9q • 9q 0. 09 . The uncertainty in the. subrange constants determined from figure 60 was 10-20%. Although no information concerning the phase relationships between temperature and humidity were obtained for this work, it should be noted that for their BOMEX 0q data, Leavitt , and Phelps and Pond show only small negative phases at lower frequencies than the BOMEX 9q phases. The negative phases indicate that the temperature leads the humidity. A summary of the cospectral subrange constants is given in Table 7. 5/3 ' • •■■;.■ • 4. 7 k Spectra and Comparison of Flux Techniques • • ' ■'■■■- •■ '■>."•• '; .: ;H ' ■ In this section comparisons are made between the different flux estimation techniques discussed in Section 2. The assumptions invoked to simplify the budget equations of kinetic energy and scalar variances are also examined. The directly calculated fluxes of momentum, 233 sensible and latent heat used as a basis for the comparison have been presented in Tables 2 and 4, and discussed in Sections 4. 3 and 4. 4. 4. 7a Comparison of eddy correlation and inertial dissipation techniques Momentum Flux Two basic assumptions invoked for estimation of momentum flux by the inertial dissipation technique are that the budget equation for kinetic energy may be simplified to the forms given by Eqs. (24) or (25), and that the one-dimensional horizontal velocity spectra is represented by a -5/3 power law behavior as shown in Eq. (11). Eqs. (24) and (25) suggest two forms for the dimensionless viscous dissipation giben by $ = (1-16 z/L)"1/4 - z/L (57) ei $ - (1 + 0.5|z/L|2/3)3/2 (58) €2 . -.-_. The expression for is derived from the assumption that total production (mechanical + buoyant) is equal to dissipation of o n ■ ' • • • • : ,' i ' mechanical energy. Wyngaard and Cote. have obtained the expression . ••K.vV.-. for $ from Kansas data as discussed in Section 2. 6. C2 The velocity power spectral relation of (11) can be rewritten as 234 5/3 2/3 k (k) (Kz) ' uu ~zrm = au (59> u,

given by Eq. (57) or 2 — (58), and u, = -uw . In figures 62 and 63, average velocity spectra from all the cruises are normalized as given by Eq. (58) divided by a , and u plotted logarithmically versus log k , the radian wavenumber in units - 1 '2 cm . The u values for the SOMA and MIT OS I spectra have been -3 calculated based on an assumed C = 1.3 x 10 , and those for the MITOS III and OWAX directly measured and corrected for pitch as discussed in Section 4. 3. In figure 62, (J> from Eq. (57) is used in the 6 1 normalization, and in figure 63, from Eq. (58). The value of the €2 subrange constant used in the normalization is a =0. 53 from direct u dissipation measurements to be presented in the next section. Also shown in figures 62 and 63 is the hot-film velocity spectrum from OWAX 4 for comparison with the average sonic anemometer spectra. A constant value of 1 for the spectra indicate a slope of -5/3 and agreement between the direct and inertial dissipation methods. It should be noted that a value of 1 (one) is not an exact agreement between 2 the two methods since the directly calculated u,_ values were used to calculate the values of 3>, . FIGURE 62 5/3 k ' average horizontal velocity spectra 2 -2/3 normalized with a u, $ (Kz) plotted u 1 versus radian wavenumber (ordinate represents agreement between direct covariance and inertial 2 dissipation estimates of u_J - :-/.:*' '■ ■ . " '■•'••'■ ';•■■'■ ' . • 236 + *T 4- G v + X <<*r + X<8T] <£x + 5^ . 7 X ^4 ^ + " X ^ < ^ t X v <3 ^ •^ X *sr j) >|(>|) 2/2 ^ 2 ' 2/2 2/S nn CO FIGURE 63 5/3 k average horizontal velocity spectra 2 -2 /3 normalized with a u , »$< + ^ . o tii ii — i — I 1 prrrn — i — r O IT ri "i "i "i — r ■:-.-;■:•:.;■■■:■■■, ■ ■ o CM I _ o ro I C.) or LJ CD i _ o ro OJ i «st- O CD 0 >1 00 nndi> 239 From figure 62 the constant spectral levels and the corresponding interval for the spectra are SOMA (1. 7) and MITOS III (0.93) for 0.02 .£:•■ " ''■ - .'- '."•■ •':'••■*'• -' '-••.•■ '■■■■ inordinately high. Matching the MITOS I x-wire to cup anemometer results may have also introduced an error contributing to high spectral levels. From analysis of the OWAX sonic and cup anemometer mean velocity 240 measurements, the mean velocities agree within 4% except for the OWAX 3 run which indicated 5-7% cup over-speeding. Analysis of the MITOS III hot-film and cup data indicated up to 15% cup over- speeding. This over -speeding for MITOS III may be high since the hot-film was mounted horizontally with respect to the flow field instead of vertically as was done for the OWAX 4 hot-film. Wyngaard and 37 Cote used a 10% correction for cup over- speeding for their Kansas velocity data based on analysis of the Kansas cup anemometer measurements by Izumi and Barad (1970). Hyson (1972) " and 64 Kondo et al (1971), suggest that cup over-speeding is 1% or less, 64 however, Kondo et al indicate that up to 4-7% cup over- speeding -3 over land may occur in the daytime. If a value of C = 1. 5 x 10 and a 10% cup over -speeding correction is applied to the MITOS I data, the subrange spectral levels would be 0.8 (figure 62) and 0.61 2/3 (figure 63). This correction does not include the effect on <£ due £ to changes in the z/L values but the differences are not significant (<5%) . Using the corrected values for the MITOS I spectra and the MITOS III and OWAX result, the average spectral level for figure 62 is 0. 83 ± 0. 07 and for figure 63 is 0. 64 ± 0. 004 . The confidence limits only reflect differences in the average corrected spectral levels and as such are probably low. Better confidence limits for the spectral 2 levels would be ~ 30% referring to the coiifidence limits on u., in 24.1 Table 4, The trend in the values indicates that for this work the 2 inertial dissipation method underestimates the value of u, . The underestimation is more pronounced using the $ expression C2 37 8 proposed by Wyngaard and Cote'. Pond et al obtain good agreement 2 • between directly measured u values (corrected for pitch by the "R (f) = -0. 5" method) and the inertial dissipation method usina an u\v ' ° a - 0. 55 and the expression u, = [K (€-B) z] $ " (60) -•- m derived from Eq. (22) assuming no flux divergence, where B = g w9 T -3 — (—3 + — x 0. 47 x 10 wq) (equivalent to the second term in Eq. (22). rp & I -> o Pond et al, however, do not include the effects of stability on the mean velocity profile (3? ) in their calculations. Including the <& in m 2 dependence in their calcinations would increase the u values obtained by the inertial dissipation method by 2 5% . For near neutral conditions (-z/L <0. 1) Miyake et al 33 (1970) apply the inertial dissipation technique with the assumption that ■ production and dissipation are in equilibrium (Eq. (3)) and obtain higher 2 values of u_, than those obtained by the eddy correlation technique. 36 From measurements over land Hicks and Dyer (1972) obtain a value of a - 0. 54 using the relationship given by Eq. (56) with the u, values u obtained by the eddy correlation technique and confining the estimates ' ■- ■ ■ • '.■■/' 242 2 of a to conditions of u, >20 cm/sec and H_ > 10 mw/cm . u •>■ S The subrange spectral levels of figures 62 and 63 are also an indication of the ratio of dissipation of mechanical energy to production (including stability effects for production). Using the inertial dissipation technique to obtain the dimensionless dissipation and ($ -z/L) to obtain the dimensionless shear production, Leavitt m fhids a 7% difference (production greater) between the two for a. - 0. 53 (a value of~0. 96 on figure 61). Leavitt also finds the dimensionless turbulent transport to be approximately half of that found / 37 by Wyngaard and Cote . If this additional correction were applied to "11 Leavitt' £ results on figure 62 it would correspond to a value of approximately 0. 80 (average of 0. 96 and 0. 64) in agreement with the value obtained for the results from figure 62. It should be noted that if a similar correction were applied to data from this work the results would be lower than those obtained from figure 62. Heat and water vapor flux The assumptions required for estimation of heat and water vapor flux by the inertial dissipation technique are similar to those » employed for estimation of momentum flux when applied to the scalar variance equations and spectral relations. Also required are the assumptions that the eddy transfer coefficients for heat and momentum, and water vapor and momentum are equal and the dimensionless scalar gradients for temperature ($ ) and humidity (<£> ) are equal. The expressions for the temperature and humidity spectra from Eq. (12) can be rewritten as 243 k5/3 a (k) (Kz)2/3 Pn (61) and 2T.„ * $ k5/3 1> (k) (Kz)2/3 ^- fl. (62) 2 q;,t a $ ■1/3 "q where the starred quantities are calculated by Eq. (6) using directly ' -1/2 measured covariatices, <& °" <£ = (1-16 z/L) , and <£ as by Eq. (54). The difference between <& , and <3> will not be € 1 62 significant for comparison of the temperature and humidity results. Estimates of B vary considerably from values of 8 O on L c 0.40 (Pond et al ), Wyngaard and Cote " , Pacquin and Pond (1971), to values of 1. 0 or larger suggested by the results of Leavitt of 14 47 0n =" 3.0; Stegen et al (1973), and Gibson et al obtain /3 =* 1. 2 using the direct dissipation technique. Boston and Burling (1972) and Boston (1970) suggest B - 0. 8 for direct dissipation measurements over a mud flat. Values of B from direct dissipation measurements 0 Cor this work are presented in the next section and vary from 0. 7 to 2.4 . There is a dearth of values of B in the literature from open q >cean measurements and include estimates of B =0.4 by Pacquin q ■,-v:.-: :•■ .••■••■'• 244 and Pond and Pacquin (1972) ' using second and third order structure functions, and £ =0.25 suggested by Lcavitt' from flux profile measurement results of Paulson et al which imply $• = <3> * <2> E m H the B and |3 values given above are based on the definitions of scalar W q variance dissipation from Eqs. (3 0) and (33). Temperature and humidity spectra from the cruises normalized in the manner of Eqs. (61) and (62) are shown in figures 64 and 65, plotted versus log k(cm ) . A constant value of the' spectra indicates a spectral slope of -5/3 . Due to the variation of B and 0 B estimates as discussed above, the normalized cospectra have not q been divided by the subrange constants as was done for the momentum flux comparison. The value of the spectral levels thus represent the implied B or B required for agreement between the inertial 2 2 dissipation estimate of T_,_ or q , , and the value determined from direct covariance measurements. Since directly measured covariances are used to calculate and the implication is not exact. For H C ^ given values of B and 8 , the spectral levels divided by those values represent the ratio of scalar dissipation by the inertial dissipation technique to the scalar production assuming $ = $ = (1-16 z/L)"1/2 . The normalized temperature spectra of figure 64 exhibit considerable differences. The thermistor temperature spectra from the SOMA cruise and OWAX 2 and 3 runs exhibit a roll-off in spectral FIGURE 64 5/3 k average temperature spectra normalized 2 -1/3 -2/3 with 2 T, <1> $ (Kz) plotted versus * H € ^ radian wavenumber (ordinate represents /? required for agreement between direct covariance 2 and inertial dissipation estimates of T\,,) ■■.-.■ ...,':' ''.'•'/'' 246 \ TTTT_1 — f- O o - o ~ o X "1 ii rn — i — t rrrrrT O CM i O or > to I - O CM ■ ^ o CM I £/i H * $ / 9./Z i ■ 2,fW ee,. FIGURE 65 5/3 k average humidity spectra normalized with 2 -1/3 -2/3 2 q^ 3> $ (Kz) plotted versus radian wavenumber (ordinate represents /3 required for agreement between direct covariance and inertial dissipation estimates of q ) '"■••■ ■ .'.-.j N 248 i i i 1 i — i — i r (TTTt i ' i — i r O 1 • . g 9 3T O CVJ i bb. £/l -* V>z*z/s,f*WW * 249 level for k > 0. 03 cm due to instrument response. The cold wire spectra are still increasing, however, and do not exhibit constant spectral levels below k = 0. 8 cm with the exception of the MITOS I data. The MITOS I spectrum exhibits a constant spectral level of 2. 1 ±0.2 (implied B ) over the range of wavenumbers 0.06 0. 04 cm are due to instrument response. The high spectral levels of the MITOS III data for k >0. 04 cm" may be due to high frequency noise in the humidity signal at lower frequencies than the filter cut-off (Nyquist frequency). The average implied B for this work is 0. 21 ± 0. 05 , which is lower than the value obtained by Pacquin and Pond, and Pacquin of 0.41. The value of B = 0.25 11 suggested by Leavitt is comparable with the value of 8 from figure 6 5, and suggests <1> = <3? , if production and dissipation of E m humidity variance are equal. This implies water vapor is transported more nearly like momentum than heat. Referring to the results of Section 4. 6 and the expression for O. I OL given by Eq. (53), the ratio of the cospectral constants w9 wq for heat and water vapor flux implied B ~" 13 B . Using average 6 q values of B =* 2.24 and B ^ 0.21 , the result is B =" 11 B ' 8 q 6 ^q . . ■ . ■ • • ■ ■. . .■'••••..'. .-.•.«> '■••;■ not significantly different than the result predicted by the cospectral subrange constants. 4. 7b Comparison of eddy correlation and direct dissipation techniques Estimation of the fluxes of momentum and sensible heat by the direct dissipation technique have been made from measurements of 252 the mean square time derivatives of velocity and temperature. The mean viscous dissipation (€ ) and mean dissipation of temperature variance (\ ) , calculated using Eqs. (13) and (14) from the MITOS I, MITOS III and OWAX 4 data are given in Table 8. No corrections for 69 Hekstad's (1965) modification of Taylor's hypothesis have been 37 applied as was done by Wyngaard and Cote " , since the corrections are typically < 2% . The € and x Q estimates for MITOS I were obtained by 51 Steve McConnell by matching high frequency spectra of velocity and temperature time derivatives to the converted velocity and 2 2 temperature spectra ($ (f)xf /(2tt) ) shown in figures 14 and 28. 9 9 The xfl values for MITOS III-2 and OWAX 4 from McConnell * are calculated for shorter time periods than the direct covariances but are representative values for the runs. The MITOS III e value is an average from three estimates at the beginning, middle and end of the 51 run, and the OWAX 4 (McConnell) value is from the beginning of the run. All the € and \ values have confidence limits of approxi- 9 mately 20% or better. The O and B values shown in Table 8 were ... u 9 .... . • ,, ..-•; r;:-..\ • ■ _ _■ .• '.• •/'?•". i ■■■'.■■.-'■,■ ■;•>'.;•';./: calculated using the directly measured e and \ estimates and employing the relations _2/3 1/3 *. . (k) = a € k (63) uu u 253 TABLE 8 - Direct Dissipation Results xe °u ^e 2 3 2 (cm /sec ) (°C /sec] MITOS I 1 117' 8. 6x10 "4 0.53 2.4 7 108 8.6 x 10"3 0. 50 1. 9 -4 MITOS III 2 21.2 6.3x10 0.53 0.6! OWAX 4 43.3 2.6 xlO"3 0.54 0.67 .-■... . . -. ■- 254 _-l/3 1/3 *ee(k)= ^e xe'F k (64) where u and 0 are spatial derivatives by Taylor's hypothesis. Velocity and temperature derivative spectra from MITOS I- 1 and 7, 5 1 and OWAX 4 are shown in figure 66, 67 and 68 (from McConnell). — -2/3 — — -1/3 The spectra are normalized with C (velocity) and v e 0 -1/3 (temperature) and multiplied by k so that the spectral levels plotted linearly represent a. and fl , and a constant value indicates a + 1/3 slope. The abscissa is given as log (77 k) where 77 is the 3-1/4 Kolmogorov microscale (v /c ) , and 10 (77 k) ^ k (for reference to figures 62 through 6 5). The derivative spectra exhibit a subrange behavior similar to that shown by the velocity and temperature spectra of figures 62 through 65, with the MITOS I temperature derivative spectra exhibiting an extensive inertial subrange and the OWAX 4 temperature derivative spectra having only a narrow subrange. The fi values from the MITOS I derivative spectra are comparable to the 0 implied ff values. The MITOS III (Table 8) and OWAX 4 /J values 0 0 are much lower (by a factor of 3) than the implied /3 values. The 0 v values determined by the direct dissipation technique do not 0 require the assumption that production is equal to dissipation. The direct /S values are mainly dependent on the shape (area) of the 0 - 0 . spectrum and the direct \ and e values. Since the 0 -spectrum 6 FIGURE 66 -1/3 MITOS 1-1 and 7 k velocity derivative 2/3 spectra normalized with € plotted linearly versus normalized wavenumber (Tjk) (ordinate represents a from direct 50 dissipation estimate) (from McConnell, 1974) ■• . ' >'r;:' '.''.''' '" ; ■"■ •••. '• ': •-»» >:'■ •■ 256 o° o o o o o D o o o CP o rfl- O co r ° ° n ° ofJ O G O o o o a 3 "J a ca n o a D .) 10 o a> CO e w ° E O ° u a a a D D D /v. CK O CD CO E o O O CO a. to o -5— F o Q- O Eb O D D D D C. o D

O. 0) to .(-» to •n. h- \ CM r» F E E 1 1 O o o to o O CO O ro N o ;> LO C\J ro i ii II n /\ u zs Vi/ N D o o ^o o o ■■;* : to O o O O o 8 • - O o eg o o CM i . o to I to CD o o 6 (^)n D FIGURE 67 -1/3 MITOS I.-1 and 7 k temperature derivative spectra normalized with -1/3 XQ£ plotted linearly versus normalized wavenumber (?7k) (ordinate represents /? from direct 9 50 dissipation estimate) (from McConnell, 1974) *':'■ .''•'■'■• ' ■ ■■ 258 O .< % o o o CD IV! O o o. (.0 P v^ * 1- F •o E H c> o X m O CO CD O o o r- CO 10 2 II II X N I o Q. o i a 9> o o o o o o o o o o o o to cO u o o o D ft O, □ D D D D n a n B D D □ D O <3> CO e o O ro ID it V o o> CO o o fO 'O :< CD E o O C a) ro ii ii X N O O D 93 .,n "cr -;f o O q cvi i o ID sP° a C£> 0 cP D □ $, D D fi't;'v ^ % 4 D CM i t o o ro I. i O O co • ,•••>■ O o o lO 6 o o • o 0. ( » W FIGURE 68 -1/3 OWAX-4 k velocity and temperature 2/3 derivative spectra normalized with € -1/3 (velocity) and XQf (temperature) plotted D linearly versus normalized wavenumber (Tjk) (ordinate represents a or /? from direct U 9 50 dissipation estimate) (from McConnell, 1974) r''',-'-;/ ' •:.'."■ :■-.- ■' ■"■ :;■ \ 260 o (X) 6 D % cP D rEr D D D D o o a & D Q s o o J? o o o o o o D 13 ~cr o D D D O O o G o D O c D O O o to y ... jo P o =b CL TT ) O o o o o° o o o o b O CD 6 o ID 6 o 10 E o CO O a to •^ CO O o E o O £ in O ■x p- •e- U '- n CO il •\ D to II Pr p- \u X o D 5 a J£ t n D -Q. s' D D - — o o o ro O O c\J o o o — o d 6 (v^rtf 4(>jfc)no o o cvi 5, O ro i O o ro * «: .' Ota 261 for OWAX 4 is displaced to the right of the u - spectrum, a larger relative area is obtained to determine \Q which results in a smaller 9 value of 8 as compared to the MIT OS I 9 - spectra and 8 values. 9 Gibson et al obtained a value of 8 = ll 17 from BOMEX 9 data using the same procedure as used above to calculate 8 . At the 1 6 time, the 8 value was considered high, and two possible explana - tions for the high value were suggested. The first explanation was that an anisotropic temperature field (estimated by S (— ) , skewness of dx 9 ) would enhance vertical temperature gradients if positive skewness values were observed, resulting in higher B estimates. Skewness 9 50 values for the temperature spectral derivative (from McConnell) averaged 0. 81 for the MITOS I data and 0. 84 for the OWAX 4 data, not significantly different. Both skewness results indicate similar anisotropic conditions. The second explanation was that B would increase with increasing intermittency of € , estimated by the factor 1 1/3 (— K) , where K is the kurtosis of du/dx . Kurtosis of du/dx 50 (also from McConnell) from MITOS I and OWAX 4 were ~19 and 2 3 respectively, so that the higher kurtosis values did not correspond to the higher 8 values. The higher B values from this work may be ,; .. , , . .• ■ 9 ■■..,.... © ■ • • ■ . due to the effects of anisotropy of the temperature field when compared to similar measurements over land (dry conditions), however, other effects besides anisotropy and C intermittency are required to explain differences in the 8 values from the different cruises. 9 262 Results of calculation of momentum flux ai i nsible heat flux by the direct dissipation method for MITCS I, MIT II, and OWAX 4 are shown in Table 9 for comparison to the directly measured covariances. The direct dissipation estimates of u and wG were calculated using Eqs. (7) and (8), rewritten to include corrections for stability effects as %- $ (66; For Eq. (6 5) the two expressions for <& given in Section 4. 7a are also compared. The u_,_ values used in Eq. (66) are the direct dissipation estimates for z/L = 0. The expression for 3> was used in Eq. (66). The direct dissipation estimates of u for MITOS I are all higher than the calculated direct covariances suggesting the assumed -3 -3 values ofC =1.3x10 is low. If a value of C = 1. 5 x 10 is used and a 10% cup over -speeding correction is applied (as in Section 4. 7a) to the direct dissipation estimates, the results for MITOS I are comparable to those from MITOS III and OWAX 4. It should be noted that the confidence limits for the direct covariances are ± 25% and for the direct € estimates ± 20% so that comparisons between the two methods will only refer to trend; using the values of Table 9. The 263 W < to o; 0 cr 0 ro (M 0) H o (3 w o N •H 4J « ■ r-i w (0 • l-< p u 0 (3 o Ctf o U w «+-4 o £ o en •H IN rt s o in © + ro ro ro II ro w o ii ro * ro P 4) CO \ ■— * -$ 1 d W •9" W X CD <& X ro •" . — II £ £ o II -1 - N- 2 CD CD o ro in oo CO ro CO O H o ■* a o ro ■* < is- 264 same is true for the w9 estimates with better confidence liinits on the values obtained from the two methods. 2 Best agreement between the values of u is obtained using z/L = 0 for the direct dissipation calculations! Including the 2 MITOS I results corrected as suggested above, the v. estimates using $ are an average of 12% higher than the direct covariances, € 1 and the estimates using $ are an average of 13% lower. The ^2 results indicate that the dimensionless turbulent transport is. 33 approximately half of that suggested by Wyngaard and Cote t and in agreement with the results of Leavitt for turbulent transport from BOMEX measurements. The direct dissipation estimates of w6 are significantly higher than the direct covariance measurements. If the 10% cup over-speeding correction is applied to the MITOS I w9 estimates, the direct dissipation results for all the data are higher than the direct covariances by an average of 30% for z/L = 0 , and 77% when stability corrections are included. Differences between the w6 values for the two methods cannot be accounted for by uncertainties in the pitch corrected covariances and the xQ anc' ^ estimates, ■ .-.■"'.'•..-. particularly when stability corrections are included in the direct dissipation calculations. The results support the evidence from the previous section that dissipation of temperature variance may exceed production by a factor of 2 or more. 265 14 Stegen et al (1973) used the direct dissipation technique to estimate momentum flux and sensible heat flux from high frequency hot-wire and cold-wire velocity and temperature measurements. Using the stability expression <& to correct the direct dissipation estimates 2 14 2 of u_,_ , Stegen et al obtain an average value of shear stress of ~ 2 0. 39 dynes /cm , somewhat lower than the eddy correlation results o reported by Pond et al of 0.49 (Univ. of British Columbia result) 2 and 0.44 (Oregon State Univ. result) dynes /cm . If the results of 14 Stegen et al for 6. 7 m. (-z/L s" . 26) were corrected for stability effects using the expression <5 (Eq. (57), the estimated stress would be 0. 39 dynes /cm , in better agreement with the direct covariance results. It should also be noted that the direct covariance results were corrected for pitch using the R = - 0. 5 technique to estimate uw the rotation angle. The analysis of Section 4. 3 suggested that this method may tend to overestimate the correction under certain conditions, however, not riecessarily applicable to the BOMEX results. 14 Stegen et al did not apply stability corrections to the direct dissipation estimate of the sensible heat flux since the variability in the v estimates were considered greater than the errors 6 due to neglecting stability effects. As a result, a value of H = 0. 74 ? 8 mw/cm was obtained, lower than the results reported by Pond et al 2 of 1". 0 (OSU) and 1.3 (UBC) mw/cm from direct covariance measurements, also using the R - - 0. 5 correction. If stability 266 14 effects are included in the calculation of Stegen et al (using 6. 7 m 2 atid - z/L = 0.26) , the resultant H = 1.25 mw/cm , in agreement with the direct covariance measurements. This result is much lower 2 than the OSU inertial dissipation estimate of H =2.8 mw/cm using a |8 = 0. 4 ; for /? = 1 . Better agreement is obtained with a 0 0 corrected value of H =1.1 for the OSU inertial. dissipation estimate of the sensible heat flux. Although there appears to be agreement between the direct dissipation estimate of H„ when stability effect are included and the direct covariance measurement, the absolute spectral,levels for the OSU, UBC, and UW (Univ. of Washington - Leavitt) temperature spectra did not overlap with the low frequency 14 portion of the UCSD (Stegen et al ) temperature spectra (personal) communication, Leavitt, Friehe). Differences between the two sets of spectra may have been due to spatial resolution effects at the high end of the low frequency spectra (OSU, UBC and UW), and high pass filtering effects (below ~ 2 Hz) at the low end of the high frequency' (UCSD) temperature spectra. As was mentioned earlier, the MITOS I cruise had conditions similar to those of BOMEX, and the high frequency temperature spectra 5 1 — (McConnell) used to obtain \ estimates were matched to the 0 temperature spectra presented in Section 4. 5b so that any differences due to calibrations would be eliminated. 267 4.7c Scalar variance budgets reexamined A basic assumption common to both the inertial and direct dissipation techniques used to estimate the fluxes of heat and water vapor, is that production of temperature and humidity variance is equal to dissipation (Eq. (4)). For open ocean measurements, this assumption may not be valid. Production and dissipation of temperature variance were calculated for the cold wire runs and the results are given in Table 10. The \ values obtained by McConnell 8 50 (1974) and given in Table 8 were used to calculate the dissipation. Production was calculated from the relationship derived by combining Eqs. (4), (6), (8) and (19) and written as df T* U* -w9- "d7~ ~ aKz *H " (67) Similar results for humidity were not obtained since v could not be q determined from humidity measurements, due to the limited frequency response of the Lyman-Alpha humidiometer. Calculations of production of temperature variance were based on a - 1. 0 (KTT = K ) , K = 0.4 , ■ : H m -1/2 $ = (1-16 z/L) , and T and u , from direct covariance H ~'~ ;,: measurements (MITOS I u, from an assumed C) . Ratios of . , . . - !* D ■ ;• '-...• dissipation to production are also given iii Table 10. For all the cold wire runs, dissipation of temperature variance is greater than production. The smallest ratios for dissipation to production from MITOS I of 2. 6 would be increased to TABLE 10 268 Production and Dissipation of Temperature Variance Dissipation 2 2 Production (° C /sec) Dissipation (° C /sec) Production MITOS I -1 1. 7 x 10 -4 ■7 1. 7 x 10 4. 3 x 10 4. 3 x 10 -3 2.6 2.6 MITOS III- 2 0. 83 x 10 3.2 x 10 OWAX 4 2. 9 x 10 -4 1. 3 x 10 -3 4.6 Production = -w9 df T* U> dz ttKz (1 - 16 z/L) 1/2 Dissipation =■ &?;■•*•.: '•■'-■■■,'.:.■:•'•':-■•.; .\ 269 about 3 if a 10% cup over -speeding correction is included in the calculation of \ . The values of production for the MITOS I runs would not be significantly affected by an increase in u0, if a value of -3 C = 1. 5 x 10 were used, since $ would also increase, and u m the increase in and u would be balanced by a comparable m ;': 2 decrease of T . Although dissipation of humidity variance was not directly measured, results of Section 4. 7a indicate that production of humidity variance may be larger than'dissipation. Using a value of B - 0. 4 , q and $ = <£ , Leavitt obtained equal production and dissipation rates for humidity variance. The average implied B ^ 0.21 from comparison of the direct covariances and estimates of the inertial dissipation technique, suggests that for a given B = 0. 4 , production is greater than dissipation. If the expression for *■ 3> and E XT <& ^ "l> as suggested by Leavitt' s flux profile analysis, the xL M. implied B would be more nearly equal to 0.4 if production eqxials dissipation. From the direct and inertial dissipation results for temperature and the inertial dissipation results for humidity, a reconsideration of the assumptions used to simplify the scalar variance budgets seems appropriate. Eqs. (29) and (32) were obtained by assuming horizontal homogeneity and stationarity. To test the assumption of horizontal homogeneity for the temperature variance 270 — dT budget, term - u9 ~7"r "as to be considered. For the OWAX 4 run, a horizontal temperature gradient of approximately 5° C per 100 m. would be required to balance production and dissipation. This gradient is far greater than would be expected over the ocean or seen in the OWAX 4 time series of Section 4. 1. Althbugh non- stationarity may have affected the temperature results for the SOMA cruise due to the small heat fluxes measured, non-stationarity effects for the other cruises can be expected to be small as noted by 37 "' Wyngaard and Cote " for over -land temperature measurements. Two terms which appear in the temperature variance budget and not included for Immidity are the heat transfer due to radiation, 20 R , and the heat transfer due to viscous heating, 29c /C . Effects of the terms were considered in Section 2. 4. From P the previous discussion it appears that the viscous heating term may be neglected. Effects of radiative heating/cooling for BOMEX conditions have been discussed by Leavitt, Phelps and Pond, and 8 10 Pond et al. Phelps and Pond suggest that absorption of longwave radiation by the increased water vapor concentrations in BOMEX would tend to produce a more homogeneous temperature structure and cause suppression of large scale temperature fluctuations. This would not explain the larger differences between dissipation and production for the U-ss humid OWAX cruise. As mentioned in Section 2.4, maximum 2 destruction of 9 occurs at small scales (dissipation scales) for 271 42 internal radiative transfer (Townsend, 1958). If 20K.' were included as a dissipative term for this case, the difference between production and dissipation would be increased. Leavitt suggests that the effects of cooi.ing by radiative flux divergence measured during BOMEX may account for differences between the temperature and humidity signals, the spectra and the cospectra. Leavitt' also suggests that the cooler air at heights between 50 and 400 m (as evidenced in the BOMEX potential temperature gradient) due to radiative cooling, descends by negative buoyancy adjacent to the backs of warm plumes and causes the "cold spikes". As shown in figures 7 and 9, the same phenomenon (cold spikes) are also observed for both the warm, humid conditions of MITOS I, and the cold, less humid conditions of OWAX 4. From the OWAX 4 production-dissipation results, radiative cooling alone could not account for the differences between production and dissipation for both tyjoes of conditions. The scalar flux divergence terms for the temperature and humidity budget may amount to 25% and 10% of the production as 11 37 suggested by the results of Leavitt, and Wyngaard and Cote (temperature). The magnitude of temperature flux divergence is not sufficient to account for the differences between production and dissipation. If a humidity flux divergence of 10% of the production is assumed, it would result in a decrease of the implied B values and q 272 lend more support to the suggestion of Leavitt that <£>=<£ E m 44 Temperature profile results of Paulson et al implied <±> =0.4 H 1/2 (1 - 16 z/L) . This expression for would result in a greater ri difference between dissipation and production than obtained using -1/2 $ - (1 - 16 z/L) , to balance the production and dissipation -1/2 results would require '- 4 (1 - 16 z/L) , highly unlikely. The remaining terms in the scalar variance budgets are the source /sink terms, S^ and S , which represent contributions or 9 q losses to the variances due to interaction or possible effects of spray on the temperature and humidity fields. It is proposed that the evaporation of spray can account for differences between production and dissipation of temperature variance. Evaporation of spray in 51 conjunction with the ramp model proposed by Gibson ct al can explain the ramplike structure of the temperature and humidity time traces , and can also explain the cold spikes in the temperature signal and the associated behavior of the humidity signal. Upon careful examination of the temperature and humidity time traces, they may be represented as shown in figure 69. The associated vortex structure shown below the temperature and humidity signal representations is 51 an end view of the horizontal roll vortices of the Gibson model. The wavelength of the ramps is shown as 100 meters representing the large scale ramps in figures 7, 8 and 9. The 5 m. ramps shown by 51 Gibson et al are not inconsistent with the fine scale structure shown FIGURE 69 Ramp model for temperature and humidity over the ocean ■ • ■'■,'rV •' • , ■;■'.: 274 warm, humid conditions (MI10SI, BOMEX) TEMPERATURE HUMIDITY -100 m ombient temperature ombient humidity w,z U, X cold , dry conditions (OWAX 4) TEMPERATURE HUMIDITY ombient temperature ambient humidity 100 m 1.6.4.416 275 in the magnifications of figures 7 and 9. Water droplets of spray accumulated in fine sheets along the interfaces of the roll vortices evaporate, causing the "cold spikes" of the temperature signals. The additional source of evaporation which increases the temperature variance can account for the difference between calculated values of production and dissipation of temperature variance. Since the air above the vortex is dryer than the air within the vortex, evaporation occurs on the outer edge of the vortex cooling the overly ing air. The maximum accumulation of air cooler than the ambient temperature will then be forced down at the leading interface of the vortex due to the negative buoyancy of the cooler air and the structure of the roll vortex. The descending cooler air at the leading edge of the vortex causes a cold spike, and the excess water vapor due to evaporation causes a "rounding" of the corresponding humidity minima at the interface. The small amount of "smoothing" of the humidity signal at the lower part of the ramp interface may also be due to the Lyman -Alpha humidiometer measuring a combination of water vapor and spray which has accumulated at the vortex leading edge or effects of frequency response limitations. The amount of water vapor required to account for the difference between production and dissipation is small due to the high value of the latent heat of vaporiza- tion. Similarly, the amount of water droplets required would also be small. Differences between the temperature time traces for the two 276 cruises will be discussed in detail in Section 5. 70 From a laboratory study conducted by Wu (1973) , the concentration of water droplets measured at velocities above 8 m/sec 2 indicate that less than 10 droplets per m (mean diameter ~ 150 \x ) occur at heights between 5 and 20 cm in a wind wave tank (14 m x 1. 5 m) for wind velocities less than 8 m/sec. Although it is fairly 70 73 well established (Wu, 1973, Krauss, 1967 ) that droplet concentra- tion decreases exponential]y with height above the sea surface, absolute droplet concentration for a given height and wind velocity is not known. -3 For the OWAX 4 run, a value of S = - 1 x 10 ° C/sec , • 6 is required to account for the difference between production and 3 dissipation. If S (jigm/cm - sec) is used to represent the adiabatic rate of evaporation, then S may be written as 6 L — S0 = -jr (SB) (68) 9 P C P where S = S + s (the mean and fluctuating evaporation rates). If it is assumed that s and 8 are perfectly anti-correlated 3 0 (r * = = -1 , an increase of s results in a decrease of 6) , s 8 .■ a ' c • ■ fa y • then a ' may be estimated from the relation L S~ -~~ (o- a.) (69) 0 p C s 9 P 277 -3 2 For SQ " - 1.0 x 10 °C /sec and cr = 0. I °C , a value of -3 3 a. = 4. 0 x 10 /jgm/cm sec is obtained. To determine if this value s of a* is reasonable, an examination of the time series is required, s If an average AT of 0. 1 °C for the "cold spike" portion of the temperature ramp interface is assumed, the time required for evaporation to occur may be calculated from the relation. A T At °- — — - P C (70) L A s p v ' obtained by integrating the time rate of change of the species concentration equation (for Tp C - sensible heat) and assuming the evaporation source term produces the entire temperature change -3 3 (0.1 ° C ) . For As - a . — 4x10 figm/cm - sec , the At required is ~ 10 sec . For the OWAX 4 run (U ~ 5 m/sec) this represents 50 meters, approximately half a ramp wavelength. For |r.|0.1 the time and/or distance would be larger, s 0 Assuming that evaporation occurs along a considerable portion of the vortex interface, this result does not seem unreasonable. The resulting -2.3 Aq due to evaporation is 4 x 10 /xgm/cm , much smaller than the mean water vapor concentration and yet possibly enough to cause a •■ . • ' • '■ "■■■■'■' -.■■■■ smoothing of the humidity minima at the ramp interface. As mentioned previously, due to effects of freqiiency response limitations of the Lyman - Alpha and possible sensing of water droplets, this smoothing may be 278 instrumental. For the MITOS I and BOMEX conditions, the evaporation of droplets may also be occurring in conjunction with radiative cooling as suggested by Leavitt. The combination of the two phenomenon could account for the imbalance of the temperature variance budget for the MITOS I data and the difference in the temperature signals of the MITOS I and OWAX cruises. Radiative cooling in the air above the roll vortices combined with evaporation would tend to break up the ramp structure and lengthen the "cold spike" as shown in figure 69 and in figures 7, 7a, 7a 1, and 7a2. The difference between the two time series can also explain shape of the temperature spectra and the w8 and u0 cospectra from MITOS I. The spectral and cospectral results are discussed in Section 5. 4„ 8 Application of the Bulk Aerodynamic. Technique for Estimation of the Turbulent Fie at Fluxes The bulk aerodynamic method relates mean wind speed and sea- air temperature atid humidity differences to the fluxes of latent and sensible heat by the relations ■''■-'■■■ H = p C C U AT S p wB (71) FT = L C U Aq L v wq 279 where AT is the difference between sea surface temperature and air temperature at a specific height, and Aq is the corresponding absolute humidity difference (saturated at the sea surface temperature). 2 Roll has suggested that the constants C n = C = C for near w8 wq D neutral conditions. To include the effects of stability on the mean wind shear, and temperature and humidity profiles, the expressions of (71) may be rewritten as H'pC C UAT$ S p w9 B H =" L C U Aq a L v wq B (72) where ( . The constant z represents the "roughness" m o ^ b height and will be assumed equal to one for the bulk aerodynamic calculations. Using values of a = 16 and £ = 3. 5 (Krause, (1967) , and Lumley and Pan of sky (1964) ), values' of U AT '$ ' B and U Aq $ , were calculated for each run and are given in Table 11. B Also given are the corresponding w8 and wq values by the direct covariance technique, and the C ,. and C required for agreement w 0 wq CO n r% ■ c J o 10 CD O r— i o CM O co O in 00 ■* o in CO IT) o o h CD (M 00 co o o 00 co o 00 co 4J oo oo CO I CD 0(5 PQ ■sp in ■' ■ - , - - .• .*-■ ■■ ■ o r- CO o^ r— 1 CO o o o oo r«- *tf o oo ^ m ■* o 00 CO "<* . ■•>■■< = 00 CO —i r~ 00 oo co ^t1 < o w w O O H H »—i i— i S ^ 281 between the bulk aerodynamic method and the direct estimates. _3 The average value of C is (1. 29 ± 0.36) x 10 ' in wq Q agreement with the value suggested by Pond et al of (1.20 ± 0.24) -3 x 10 for BOMEX results. For the pitch corrected covariances (MITOS III and OWAX) , C =1.03, suggesting C O < 1° , the instantaneous pitch correction applied to the data gave a uw value < 283 coinparable to results of the other two methods. The estimated pitch angles, however, were higher than the measured pitch angle. The measured a /u =2.8 ± 0. 5 , was comparable with the results of Leavitt from similar open ocean velocity measurements 55 using estimated pitch angle corrections, and Mitsuta and Fujitani using inertial reference frame corrections for ship motion. Pitch 1/3 corrected a /u , results followed the predicted (- z/L) behavior w * 11 8 and were coinparable with the results of Leavitt and Pond et al. Values of 0" /u , for this work were higher than the results of . w * C Q Wyngaard et al obtained over land. Vertical velocity fluctuations over the open ocean may have more low frequency energy containing eddies than over land as suggested by the scalar ramp model and associated horizontal roll vortices shown in figure 69. Discussion of the time series in Section 4. 1 included the observation that warm, humid air was associated with upward vertical velocity and negative horizontal velocity changes, with the opposite also being true for colder, less humid air. The associated anisotropy of the velocity field due to the large eddy structure which determines the scalar 51 field structure is supported by tho results of Gibson et al, who found positive skewness values of about 0.5 for (bw/bx) when conditionally sampled (i. e. when w ~ 0) > as compared to the isotropic value of zero. The average correlation coefficient for the pitch corrected results was r - -0.26 ± 0. 08 , also in agreement with the results of uw ■ -■■••.' ■ 284 11 8 Leavitt and Pond et al . To remove possible stability dependence of the correlation coefficient, the r values were normalized with the viw expression for the non-dimensional dissipation of kinetic energy. 2 /3 Using <3> = (<|> z/L.) , the resultant normalized value was c ~ 33 r = - 0. 25 ±0. 06 , comparable to the result of Miyake et al for uw near neutral conditions, I Velocity f - spectra, normalized to include stability effects 2 agreed within the given uncertainties of the u values with the results 11 ^ A ? / ^ of Leavitt and Kaimal et al, and followed the predicted f inertial subrange behavior. Values of 0.29 ±0.06 (horizontal velocity spectra) and 0. 40 ± 0. 09 (vertical velocity spectra) for the f - spectral constants were in better agreement with the predicted constants using the dimensionless dissipation expression for (as above). €1 Lower values of the constants were obtained using the form of 2 /3 2 /3 37 $ = (1 + 0. 5 | z /L | ) suggested by Wyngaard and Cote . Scatter e2 in the spectral results for the first two criiises was attributed to x- wire drift, possible cup over-speeding errors, and uncertainties in the -3 calculated u, values from an assumed C (1. 3x10 ) . Spatial averaging effects and distortion of the vertical sensing path of the sonic anemometer (OWAX) caused a steeper roll-off in the high frequency end of the u and w spectra for the last two cruises than the first two cruises using x-wire anemometers, The normalized pitch corrected momentum flux f - cospectra 285 I 8 were similar to uw cospectra obtained by Lea\ and Pond et al. The uw cospectra subrange constant for this work, a. = 0. 01 was uw lower than comparable estimates of a by Leavitt (0. 07) and uw 56 Kaimal et al (0. 05) . The lower a value may be due to a combina- uw tion of high frequency noise in the uw cospectra and possible distortion of the sonic anemometer (vertical path) as mentioned above. However, -4/3 the high frequency behavior of the cospectra followed the predicted f subrange slope over nearly a decade for f > 0. 1 . This indicates the N lower a value may be real and suggests that production of kinetic uw ' \ °° energy may occur at larger scales over the open ocean than over land under certain conditions. A shift of production of kinetic energy to larger scales is consistent with the ramp model, with well defined horizontal roll vortices for the colder, less humid conditions as shown in the bottom portion of figure 69. Comparison between estimates of the momentum flux by the direct covariance and inertial dissipation techniques was made using a 5/3 k ' spectral representation of the data, illustrating the approach and L: ..'. -5/3 agreement with the predicted k power law behavior required for application of the inertial dissipation technique. Agreement -was obtained between direct covariance estimates of momentum flux, and inertial and direct dissipation estimates within the uncertainties of the direct estimates, applying the assumption that total production of kinetic energy (mechanical -f buoyant.) was equal to dissipation (<£ ) . €1 286 Lower estimates of momentum flux were obtained by the dissipation techniques using the expressioti suggested by Wyngaard and Cote «P ) . The average value of the velocity inertial subrange constant C2 from the direct dissipation technique was c. = 0. 53 ± 0. 03 . Trends in the direct dissipation estimates of momentum flux suggest that turbulent transport cannot be neglected in the marine boundary layer and may be approximately half of the estimates of dimens ionless 37 turbulent transport over land (Wyngaard and Cote " ). 5. 2 Latent Heat Flux The pitch corrected wq covariances had an average uncertainty of ~ ± 10% „ Larger uncertainties could be attributed to the uncorrected wq direct estimates which were probably determined within ± 2 5% . Values of (J /a, for this work followed the predicted q * ■I/O (- z/L) behavior with C =* 0. 95 . Vahies of cr /q , were lower q q * than corresponding 0" /T values, and were lower than the a /q , r & q * q -1* results of Phelps and Pond and Leavitt for BOMEX data. The average correlation coefficient for the water vapor flux results was r = 0.43 ±0. 11 , with a trend in the r values from the colder, wq wq less humid cruises to be higher than results from the warm, humid cruises. To remove trends due to stability effects, normalized ~ 1/2 1/6 correlation coefficients (r ) were calculated, using

, for production of humidity variance equal to EM dissipation, or production greater than dissipation for <& = <& . The L H B for this work is comparable to B =0. 25 suggested by Leavitt q q 44 based on the flux-profile results of Paulson et al, and also comparable ■ • • . 7 2 to the results of Smedman-Hogstrom (1972), who obtained a value of B - 0. 29 ± 0. 10 from measurements over land in Northern Sweden, q assuming production equaled dissipation. 289 5. 3 Sensible Heat Flux Directly measured w0 direct covariances, corrected for pitch effects, were determined with uncertainties of ~ ± 10% . Uncorrected P( d x-wire drift ossible effects of direct w3 values for the SOMA cruise were subject t (in w ) , temperature calibration uncertainties, and non-stationarity for near neutral stability conditions. The average SOMA and MITOS I direct v/9 values are probably estimated within ± 2 5% , although this uncertainity may be higher for the SOMA cruise. Values of O /T, for the MITOS I, MITOS III and OWAX cruises follow the predicted (- z/L) behavior with C = 0.95 as suggested by Wyngaard et al. " The cr /T , values for the warm, 9 :,: humid cruises are higher than a /q and more comparable to BOMEX 11 ■ 10 results of Leavitt, and Phelps and Pond than the results of the colder, less humid cruises. High values of 0" /T , for the SOMA 0 * cruise were attributed to uncertainties in u0, values (from an assumed C ) and possible effects of non-stationarity. Significant differences were exhibited between average values of the correlation coefficient, r , for the colder, less humid cruises w9 corrected for pitch (r = 0. 48 ± 0.04) , and the warm, humid cruises (0. 16 ± 0. 11) , not accounted for by lack of pitch corrections for the warm, humid cruises. The r correlation coefficients were w9 normalized in the same manner as was done for the r values to wq remove any trends due to stability effects. Normalized correlation 290 coefficients, r _ exhibited similar trends as the non -normalized wo values, however, less pronounced. The higher values of r and w9 r for the colder, less humid cruises can be attributed to the well wo defined ramp structure for those cruises, illustrated in the bottom portion of figure 69. The average value of the normalized correlation coefficients was r = 0.21 ± 0. 1 , comparable to the result of Miyake 59 et al (r = 0. 24 ± 0.2) for near neutral conditions. No significant wo trend in the r „ values were observed. u9 Normalized temperature f - spectra from different cruises with different meteorological conditions did not compare with one another, and were not similar to humidity or velocity spectra. Normalized sensible heat flux cospectra exhibited similar differences, however, the w9 cospectra from the colder, less humid cruises were somewhat similar to the corresponding wq cospectra. Temperature -2/3 spectra from the warm, humid MITOS I cruise exhibited a f behavior and were similar to temperature spectra obtained by Leavitt, and Phelps and Pond for BOMEX data. Temperature spectra from the colder, less humid cruises appeared to follow a -1/4 power law behavior over nearly 2 1/2 decades of normalized frequency above f — 0. 5 . The normalized temperature spectra from the warm, humid cruises in general exhibited higher spectra levels than the spectra from colder, less humid cruises. If it is assumed that evaporation of spray is contributing to the suppression of low frequency temperature 291 fluctuations (discussed in the next section), spectra obtained at heights fai . from the surface should have higher normalized low frequency spc il levels than spectra from lower heights. Evidence of this 5/3 effect can be observed by comparison of the k temperature spectra (figure 63) from MITOS III (12. 5 m. ) and OWAX (3. 5 m. ) for the colder, less humid conditions, and comparison of 8 m. and 30 m. 11 temperature spectra obtained by Leavitt. In both cases, spectra obtained at greater heights above the ocean surface exhibit more pronounced low frequency energy. Leavitt suggested that the higher low frequency 30 m. spectral levels may be due to radiational heating of the thermocouples, however, he noted that not all periods of day - light showed the low frequency fluctuations 0 -4/3 Normalized w9 cospectra exhibited an £ ' behavior, with higher values of f ) or lower (< f ) cospectral levels than cospectra from the colder, less humid conditions. The value of f at the cross -over point represents approximately 50 meters, which corresponds to half a ramp wave- length as shown in figure 69. For larger scales than 50 meters temperature is less correlated with velocity or humidity for the warm humid conditions, and the reverse true for scales smaller than 50 meters. The "cold spike" of the warm humid conditions is not as sharp as the "cold spike" for the colder, less humid conditions, reducing the similarities between temperature and humidity (and velocity presumably) for scales larger than half a ramp wavelength. Smaller scales in the temperature field are more pronounced for the warm humid conditions as illustrated in the top portion of figure 69, associated with a "breaking-up" of the roll vortices as shown. The break-up of the roll vortices and associated ramp structure may be due to combined effects of evaporation (less pronounced for warm, humid conditions) and descending overlying cool air due to radiative cooling as suggested by Leavitt for BOMEX conditions. The a „ and a. . results a] io uG w0 suggested that vertical transport of heat is always more efficient than 293 56 the horizontal transport for smaller scales as found by Kaimal et al over la.nd; the reverse was also true for larger scales. Comparison of the inertial dissipation and direct covariance techniques for estimating sensible heat flux was made in the same manner as was done for latent heat flux. For agreement between the two techniques a value of the inertial subrange constant for temperature 5/3 of p1 =* 2 was required. The k ' temperature spectra indicated that under colder, less humid condition over the ocean, temperature may not exhibit an inertial subrange (slope -5/3) for scales correspond- ing to k < 0. 3 cm . Temperature measurements should be made out to' scales as small as 6 cm in wavelength when applying the inertial dissipation technique. As mentioned above, lack of an inertial subrange for temperature, under cold, dry conditions may be due to evaporation of spray. The inertial subrange of temperatur e is most pronounced for the warm, humid conditions, even with a shift of larger production scales toward the diffusive scales. The subrange only extends to the. point where the production scales of the associated w8 cospectra (warm, humid conditions) no longer are dominant (wQ cospectral levels go to zero). Estimates of w9 by the direct dissipation technique were higher than direct covariance estimates by a factor of 2 or more. Corresponding estimates of the inertial subrange constant for temperature, /3„ , varied from 0.7 :(- 0.07 to 2.4±0,2. From 294 direct estimates of the dissipation of temperature variance (\ /2) 0 and sensible heat flux (wfj) , with uncertainties of +20% and ± 10% respectively, dissipation of temperature variance was found to be dT higher than production (- w0 — — ) bv as much as a factor of 4 . The dz differeiices could not be accounted for by uncertainties in the direct estimates, or by temperature flux divergence which may be as much as 2 5% of production (Leavitt ). Differences between production and dissipation of temperature variance could be accounted for by consideration of sources of production usually neglected in the temperature variance budget and attributed to the combined effects of ocean spray evaporation and radiative cooling. The high p1 values from the direct dissipation technique (which 0 does not require the assumption of production equal to dissipation of temperature variance) may be due to the effect of internal radiative 42 ~T transfer (Townsend ) which tends to destroy 0 at diffusive scales or spray droplets ( more likely for the warm, humid cotiditions with higher /? values) hitting the cold wire probes and reducing the high 0 frequency response. There is evidence that spray can hit probes since • the x-wire probes for the MITOS I and SOMA cruises (warm, humid) .-: ■ - ..■'.. . - ,. ; '. . were affected by salt contamination which produced drift in the calibrations. Both of the above effects would reduce the high frequency area under the 0 - spectra and increase the estimate of £ . From, the inertial and direct dissipation results, use of the 295 dissipation techniques for estimation of sensible heat flux over the open ocean is somewhat tenuous due to the inapplicability of the assumption that production equals dissipation of temperature variance, and the possible lack of an inertial subrange. 5 . 4 Model of the Atmospheric Surface Layer Over ijlie O c e a n In Section 4. 7c a model of the structure of the dtmospheric surface layer over the ocean was proposed consisting of horizontal roll vortices with axis aligned perpendicular (or nearly so) to the mean flow, influenced by the combined effects of evaporation of ocean spray and radiative cooling. The structure of the roll vortices is determined by the characteristics of the wind shear which brings up warm, moist positively buoyant air, balanced by the negative bouyancy of cooler overlying air due to evaporation and/or radiative cooling (inversion layer). For cold, dry conditions, evaporation of spray droplets entrained in the vortex interfaces is enhanced, resulting in a more organized vortex structure, exhibited by the well-defined ramp structure in both the temperature and humidity signals. Under these conditions, the signals are more intermittent, with relatively more quiescent periods. Larger production scales of temperature and humidity variance are dominant. The roll vortices are stretched out since the negative buoyancy of cool air at the vortex interface due to evaporation acts as a cohesive agent. Cold spikes are well defined and of short duration since only a relatively small amount of mixing of warm and cold (humid and dry) air takes place at the leading (down 296 wind) vortex interface. The temperature and humidity signals are well correlated. Relatively large v values are obtained and corresponding lower /3 values due to the existence of well defined dissipative scales. The /? estimates are higher th4n over land due to antisotropy in the small scales, There is not a prcnounced inertial I subrange in the temperature spectrum since the intermediate (transfer) scales are damped by the effects of evaporation. Under these conditions, as the height above the sea surface increases, the effects of spray evaporation will be less pronounced since spray concentration decreases exponentially with height. Under warm conditions, with higher absolute humidity levels, the vortex structure and associated ramp structure of the scalars begin to break-up. Less evaporation of spray occurs and effects of radiative interaction with the temperature field due to increased water vapor concentrations tends to produce a more homogeneous temperature structure and cause suppression of large production scales. Radiative cooling in the overlying air (inversion layer) also contributes to the break-up of the vortex structure and associated temperature and humidity signals. Cold spikes are of longer duration and more spread out due to better mixing within the vortex structure. This results in less correlation between temperature and humidity (and velocity) at larger scales, and a shift of production to smaller scales. Relatively smaller \ values are obtained and corresponding higher £ values .197 due to the suppression of both large scales (long wave radial transfer) and diffusive scales (internal radiative transfer). pression of the small diffusive scales may also be due. to frequency response degradation of the cold wire probes due to increased water droplet concentration. The intermediate inertial scales are more pronounced resulting in a well defined inertial subrange for temperature. The imbalance between production and dissipation of temperature variance can thus be attributed to effects of evaporation and combined effects of long and short-wave radiative transfer. The exact effects of evaporation and radiative transfer on production and dissipation of humidity variance is not known since no direct dissipation measurements could be made. There appears to be a slight shift to smaller scales of humidity for warm, humid conditions with radiative transfer. Conversely, the larger scales are more pronounced with relatively higher rates of evaporation occurring under cold, dry conditions. From measurements over land 73 (flat alluvial plain), Martin (1972) suggests that at heights from 2-4 m. large scale fluctuations contribute more to humidity variance than temperature variance, and that the characteristic scale of the humidity field may be larger than that of temperature by about a factor of two. The model proposed above for lower levels of the marine does not appear to be in conflict with recent models of the marine boundary 298 layer. Within the last few years, studies of the structure of the marine boundary layer have become highly sophisticated with the development and application of ultra sensitive radar, reliable low level aircraft observations, and fine scale measurements of velocity, temperature and humidity. From aircraft measurements of momentum, sensible and latent heat fluxes during Operation BOMEX, Grossman and Bean 74 75 (1973) , and Bean et al (1972) (water vapor flux only) have suggested that the structure of the marine boundary layer at the 18-150 m. level consists of a combination of linear, buoyant, convective plumes or horizontal roll vortices at large and small scales, and random « 7 A cellular convective elements. Work of Konrad (1970) and Lemone 77 (1972) , based on radar soundings and aircraft data, appear to 74 77 support the model of Grossman and Bean , however, Lemone suggests that the horizontal structures observed at wavelengths from 1.5 to 6. 5 km. (near neutral conditions) may coexist with other scales 75 of motion (large and small) with increasing instability. Bean et al suggest that from humidity measurements (at 18-125 m.) smaller scales are observed on crosswind runs, indicating more than one scale may be dominant in the marine boundary layer. Their humidity time series exhibit the ramp (sawtooth) structure for along wind runs (along wind is that measured from FLIP), and a "top hat" structure is observed on 51 crosswind runs. Gibson et al note that buoyant plumes may produce the distinctive sawtooth behavior but that they are only a sufficient and ' 299 not a necessary condition for ramps to exist. 77 Lemone has suggested that the horizontal roll vortices axes may be between -5° and 20° to the left of the geostrophic wind. Leavitt suggests ~ 10° axes orientation and a wavelength of ~ 1.4 km for the roll vortices during BOMEX. The MITOS I and OWAX time series (figures 7-9) suggest that different scales can coexist within an individual ramp structure, from wavelengths of 100-200 m , down 51 to scales comparable to those of the Gibson et al model or smaller. 77 It seems reasonable to expect that scales from 1-6 km (Lemone ) may also contain smaller scales. Results of the MITOS I and OWAX cospectra analysis suggest that the dominant scale size governing the transport of heat can vary according to the meteorological conditions. The scale sizes can also vary with height as suggested by comparison of the MITOS III and OWAX w9 and u8 results for cold, dry conditions, and by comparison of Leavitt' s 8 m and 30 m temperature spectra and sensible heat flux cospectra. In both cases (not as pronounced for the cospectra), the larger scales (f < 0.01) have more energy (normalized) for Leavitt's 30 m data than for the 8 m . Loavitt ' suggests the low frequency enhancement may be due to radiational warming of thermocouples, however, he also states that not all periods of daylight exhibited the low frequency fluctuations. Leavitt ' has suggested that air-sea temperature differences ;oo and sea surface temperature fluctuations may also contribute to differences between temperature and humidtiy measured in a cold, dry environment as compared to warm humid conditions. The air- sea temperature differences for MITOS I and OWAX were comparable suggesting that this is not a significant factor. Possible coupling between internal wave events, low frequency sea surface temperature fluctuations, and air temperature fluctuations, however, may be affecting the temperature structure in at low levels in the atmospheric surface layer. Measurements of temperature over land as compared to results over the ocean indicate that the positive buoyancy generated by humidtiy differences (enhanced by sensible heat transfer) can sustain a vortex structure (ramp structure) much better when only evaporation occurs. 66 Boston and Burling's result of p = 0. 8 over a semi-moist flat 6 suggests that additional buoyancy of water vapor and corresponding evaporation may account for the higher jS value due to the anisotropy of the temperature field with a ramp structure. The positive buoyancy and lack of evaporation over dry land (ex. Kansas) may not be sufficient to sustain roll vortices when coupled with more severe surface .. 25 roughness condition, although Haugen et al have suggested that buoyant plumes can effect the heat transport process over land. In conclusion it appears that the temperature spectra (and p ( values) and sensible heat flux cospectra do not follow universal 301 similarity over the ocean. The humidity spectra and cospectra may require modified scaling than what is normally used now to follow similarity predictions and the influence of evaporation and radiative transfer on the spectra and cospectra is not clear. Differences between production and dissipation of temperature variance, and the behavior of the temperature spectra and sensible heat flux cospectra could be accounted for by consideration of other sources of production usually neglected in the temperature variance budget, and attributed to the combined effects of ocean spray evaporation and radiative heating/cooling in light of the model proposed for the lower levels of the marine boundary layer. 5. 5 Recommendations for Further Study Application of the dissipation technique for estimation of sensible and latent heat and the bulk aerodynamic technique for estimation of sensible heat requires further study. A quantitative evaluation of the influence of evaporation of ocean spray on both the temperature and humidity variance budgets and the spectra and cospectra is desirable. This would include extension of the laboratory work conducted by Wu to field experiments over the ocean to determine droplet concentrations, variations with height, and rate of evaporation for various meteorological conditions. The possible problem of water droplet discrimination of the Lyman-alpha sensor should be investigated. This could be done in conjunction with simultaneous laser spray 302 measurements. A dynamic frequency response calibration of the cold wire probes is needed; this work currently is underway in the research group at UCSD. The influence of sea surface temperature fluctuations and coupling between internal wave events, sea surface temperature fluctuations, and air temperature fluctuations also requires further study. The temperature cold spikes and ramp structure may also be associated with the above phenomena, and also correlated with surface waves. The influence of radiation on both the temperature and humidity fields also require further study. A promising laboratory investigation is currently underway at the large water-wave facility at the Institut de Mechanique Statistique de la Turbulence, in Marseille, France, 78 7Q (Coantic and Favre (1970) , (1973) ) to determine the effects of radiation, evaporation, water waves, and stability conditions on the transfer phenomenon under controlled conditions. Application of various models of the marine boundary layer for the understanding of the physical processes occurring at the interface is indispensable. It appears that various proposed models may not be in conflict with one another and that different phenomena occurring simultaneously may account for the various model types. 303 Instantaneous corrections to the turbulent fluxes based on all components of motion relative to an inertial reference frame require further study. This work is currently underway at UCSD using outputs of a Litton inertial platform (see figure 3) and techniques similar to 55 those employed by Mitsuta and Fujitani. Recent work by Friche 80 (1974) indicates that fluxes determined by the direct covariance technique using a sonic anemometer to measure velocity, may be affected by contamination of the velocity measurements by temperature fluctuations. A major effect is on the shape of the co spectra, especially the horizontal heat flux cospectra. Effects of this contamination require further study. • ■ REFERENCES Taylor, G. I., "Some p:arly Ideas About Turbulence, " J. Fluid Mech. , 41, 3-11 (1970). Roll, H. 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A. , "Effect of Temperature and Humidity Fluctuations on Sonic Anemometer Measurements, " (Paper in progress (1974). ■ ■ '• - ■ APPENDIX 1 NORMALIZED CORRELATION COEFFICIENTS Correlation coefficients presented and discussed in Section 4. 4 ■were normalized to remove any trends due to possible stability 17 dependence of the correlations as suggested by Kaimal and Haugen. The normalization may be derived from normalized variances and covariances by integration of the normalized spectra and cospectra of Sections 4. 5 and 4. 6 and applying the relation (from Eq. (2) and Sections 4. 5 and 4. 6) (a )2 = x2 = f $ (f) df = f * (f J df (Al) x J xx J xx N N and xy = f& (f) df = f $ (f ) df J xy J xy N Normalized correlation coefficients are then defined as ~ xy r = — xy (A2) (A3) a a x y where xy = f (f J df /N (A4) ' J xy N N xy and a =f* (f__)d£M/N (A 5) x ^ xx N N 313 and similarly for 0" . Using the expressions for the normalized forms of the spectra and cospectra of Sections 4. 5 and 4. 6 the normalized correlation coefficients are r uw ■ uwU^g" (z/L) uw ■ w , -1 -1/3^ -1 _-l/3, (a u 3> ) (a u $ ) $ 2/3 ~ uw e r = — uw a a u w for G(z/L)^ 1 (-z/L) > 0) r (r ) rwy uy wy y"1 uT1 K"1 (z/L) wy v * w wy ~ ~ . -l_-I/3, , -1_ -1/2.1/6. f ) (a y, <£> $ w y v w * e ' v y - H € * 1/2 *1/6 wy H c wy a a w y , for K (z/L) w (-z/L > 0) ■ E H 314 r 9q 9q 6q 6 q 9-q %' Tl* ^^ ^ -1 ,--1/2 ^1/6 <% T* *N *C > (°q 1 -1/2 .1/6. § $ ) 6q — 3) <£" 9 q 1/3 , for H (z/L) y q = l (- z/L > 0) H E ufl\ ^ greyer on of **•*£ Compare )atent ne<* ^^^ete^.ned by t^ M y " Thesis 3752 Dreyer Comparison of momentum, sensible and latent heat fluxes over the open ocean determined by the direct covariance, iner- tial and direct dissi- pation techniques.