f HIGH FREQUENCY TEMPERATURE FLUCTUATIONS IN THE ATMOSPHERIC BOUNDARY LAYER Robert Thomas Simril DUDLEY KNOX LIBRARY ^^ NAVAL POfTQRAOUATI SCHOOL MONTEREY. CALffOMUA MMO rUolbnMUUMiL OuirlUUL Monterey, Oaiifornia HIGH FREQUENCY TEMPERATURE FLUCTUATIONS IN THE ATMOSPHERIC BOUNDARY LAYER by Robert Thomas Simril September 1975 Thesis Advisor N. E. J. Boston Approved for public release; distribution unlimited. ri&cjUo UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE fWhan Data Rntarad) REPORT DOCUMENTATION PAGE READ INSTRUCT!ONS BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO J. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtltla) High Frequency Temperature Fluctuations in the Atmospheric Boundary Layer 5. TYPE OF REPORT & PERIOO COVERED Master f s Thesis ; September 1975 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORdJ Robert Thomas Simril 8. CONTRACT OR GRANT NUMBERf*; 9. PERFORMING ORGANIZATION NAME ANO ADDRESS Naval Postgraduate School Monterey, California 93940 10. PROGRAM ELEMENT, PROJECT TASK AREA A WORK UNIT NUMBERS II. CONTROLLING OFFICE NAME AND ADDRESS Naval Postgraduate School Monterey, California 93940 12. REPORT DATE September 19 75 13. NUMBER OF PAGES 57 14. MONITORING AGENCY NAME & ADDRESSf// dlllarant from Controlling Ottlca) Naval Postgraduate School Monterey, California 93940 15. SECURITY CLASS, (ot thla riport) Unclassified 15«. DECLASSIFI CATION/ DOWN GRADING SCHEDULE 16. DISTRIBUTION STATEMENT (ol thlt Rmport) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (ol tha cbttrvct tntarad In Block 20, II dlllortnt from Rmport) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Contlnua on ravaraa aid* II nocaaaary and Identity by block number) Turbulence Temperature Fluctuations Atmospheric Boundary Layer Kolmogorov Scalar Constant 20. ABSTRACT (Continue on ravaraa aid* It nactaaary and Identity by block number) Turbulent temperature fluctuations in the atmospheric boundary layer measured at 2m, 7m and 23m in Ris0, Denmark, were analyzed with particular emphasis placed on determining characteristics of the high frequency region of the spectra of these fluctuations. The shape of the high wave number one-dimensional temperature spectrum and an estimate of the DD ) JAN 73 1473 EDITION OF 1 NOV 88 IS ODSOLETE (Page 1) S/N 0102-014- 6601 | UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Kntarad) UNCLASSIFIED JutUHlTY CLASSIFICATION OF THIS PAGEWian t>»l« En<*r*ef< Kolmogorov scalar constant were determined. Comparisons of high frequency spectral regions of temperature and velocity- fluctuations were made. DD Form 1473 , 1 Jan 73 S/N 0102-014-G601 UNCLASSTFTFD SECURITY CLASSIFICATION OF THIS PACEO^*" Oof* Hni;ad> High Frequency Temperature Fluctuations in the Atmospheric Boundary Layer by Robert Thomas Simril Lieutenant, United States Navy B.S., North Carolina State University, 1969 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL September 1975 DUDLEY KNOX LIBRARY NAVAL POSTGRADUATE SC MONTEREY. CALIFORNIA ABSTRACT Turbulent temperature fluctuations in the atmospheric boundary layer measured at 2m, 7m and 23m in Ris0, Denmark, were analyzed with particular emphasis placed on determining characteristics of the high frequency region of the spectra of these fluctuations. The shape of the high wave number one-dimensional temperature spectrum and an estimate of the Kolmogorov scalar constant were determined. Comparisons of high frequency spectral regions of temperature and velocity fluctuations were made. TABLE OF CONTENTS I. INTRODUCTION - - - - - 10 II. THEORETICAL DEVELOPMENT 12 A. VELOCITY SPECTRUM- ----- 12 B. TEMPERATURE SPECTRUM ------------- 14 III. INSTRUMENTATION AND EXPERIMENTAL APPROACH- - - - - 17 A. BACKGROUND - - - - - - 17 B. TEMPERATURE MEASURING SYSTEM --------- 17 1. Sensor -------- --17 2. Bridge ------------------ 18 C. EXPERIMENTAL PROCEDURE ------------ 21 1. Location -----------------21 2. Equipment- -- ____21 a. Meteorological Tower Arrangement - - - 21 b. NPS Platinum Resistance Thermometer- -23 c. Hot Wire Anemometer- ---------24 3. Recording Systems- ------------24 IV. ANALYSIS PROCEDURES- - - - - - 26 A. SELECTION OF DATA- - .__.„_._ 26 B. ANALOG EQUIPMENT AND PROCEDURES- ------- 29 C. DATA INTERPRETATION- ------- 31 V. RESULTS- - - - - - - - - - 33 A. VELOCITY SPECTRUM RESULTS- - - - - 33 1. Calculation of £ - _ _ - _ _ 33 a. Indirect Method- -- 33 b. Inertial Range Method- 33 c. Direct Method 33 2. Normalization of Spectral Results- - - - - 35 a. Velocity Spectra -- ---35 b. Energy Dissipation Spectra ----- - 35 B. TEMPERATURE SPECTRUM RESULTS --------- 40 1. Calculation of e_- ------------40 b 2. Calculation of K ' 40 u 3. Normalization of Spectral Results- - - - - 40 a. Temperature Spectra- ---------40 b. Temperature Dissipation Spectra- - - - 48 VI. SUMMARY AND CONCLUSIONS- ------------- 52 BIBLIOGRAPHY ------- - 53 INITIAL DISTRIBUTION LIST- -------- 55 LIST OF FIGURES 1. Wollaston Wire Mounted on Probe- ----------19 2. Bridge Circuit - - - 20 3. Ris0 Research Establishment _______ 22 4. Example of Data Selected for Analysis- ------- 21 5. Analog Analysis Scheme ____30 6. Wind Profiles Runs 5 and 6 - - - - - - - 34 7. Normalized NPS Velocity Spectrum Run 5 at 2m - - - -37 8. Normalized NPS Velocity Spectrum Run 6 at 2m - - - -38 9. Normalized Energy Dissipation Spectrum -------39 10. Normalized NPS Temperature Spectrum Run 5 at 2m- - - 41 11. Normalized NPS Temperature Spectrum Run 6 at 2m- - - 42 12. Normalized NPS Temperature Spectrum Run 5 at 7m- - - 43 13. Normalized NPS Temperature Spectrum Run 6 at 7m- - - 44 14. Normalized OSU Temperature Spectrum Run 5 at 23m - - 45 15. Normalized OSU Temperature Spectrum Run 6 at 23m - - 46 16. Composite Normalized Temperature Spectra ----- - 49 17. Comparison of Normalized Temperature and Velocity Spectra- ----- -- _____50 18. Normalized Temperature Dissipation Spectrum- - - - - 51 LIST OF TABLES I. Listing of Sections Analyzed -----------28 II. Comparison of e Values --------------36 III. One -Dimensional Scalar Constant K ' ---47 ACKNOWLEDGEMENT The author wishes to sincerely thank both Professors Noel E. J. Boston and Thomas M. Houlihan for their guidance and patience in overcoming the many obstacles encountered in the research involved in writing this thesis . Special thanks go to my wife, Jan, for her patience, devotion and understanding. Thanks to Tom, Dee and Deb, my children, for making it all worthwhile. I. INTRODUCTION Several attempts over the past few years have been made to measure high frequency temperature variations in the atmospheric boundary layer. Sensors with a sufficiently high frequency response and spatial resolution have been devised to overcome the inherent problems previously encountered in trying to measure small scale, high frequency temperature fluctuations. In addition to the sensitive sensors, low-noise electronic equipment has become available to record and analyze small scale fluctuations. The object of this research was to utilize an analog analysis scheme to determine the shape of the high wave number (small scale) one-dimensional temperature spectrum and to evaluate the scalar constant, Kfi ' , which appears in the expression for the -5/3 form of the temperature spectrum In addition, simultaneous analyses of velocity fluctuations were conducted in order to obtain the necessary information ultimately required to evaluate Kfi ' . A knowledge of the small scale temperature distribution in a turbulent field has a number of applications. It is necessary when considering the heat budget which is of utmost importance in the fields of oceanography and meteorology. Sensible heat flux can be determined by the covariance of measured temperature fluctuations and vertical components of the simultaneous wind velocity fluctuations . 10 Temperature inhomogeneities in the atmosphere are one of the quantities associated with the scattering of acoustic waves and electromagnetic radiation. This scattering, which is a major concern in the fields of acoustics and optics, is often related to variations in the refractive index. Further applications of a knowledge of the small scale temperature distribution are found in the areas of physi- cal chemistry and thermodynamics. 11 II. THEORETICAL DEVELOPMENT A. VELOCITY SPECTRUM Small scale turbulence in a fluid is a feature of interest to the environmental scientist due to its effect on heat, momentum and energy transport. The one-dimensional velocity (kinetic energy) spectrum is given by u2 = S° (k)dk (C°)2.sec"1 . (7) 9 Q 6 2 k is the molecular diffusivity and k $Q (kj is the scalar dissipation spectrum which describes the distribution with 2 wave number of the rate of decay of the quantity 0 , the temperature variance. Again, according to Kolmogorov: (1) If the Reynolds number is sufficiently large there exists a range of small scale temperature fluctuations which statistically are dependent only on e, v, efi (the tempera- ture dissipation rate) and k. Once again dimensional analysis yields •H u •H 0) »d •H PQ CM U 2 20 C. EXPERIMENTAL PROCEDURE 1 . Location The data were collected at the meteorological field site operated by the Meteorological Group of the Danish Atomic Energy Commission, Research Establishment, Ris$. The site features a 130M meteorological tower instrumented at seven levels. In addition, miscellaneous instrumentation can be mounted at arbitrary levels provided only that the electronics is sufficient to drive the cables from the instrumentation to the junction boxes at the seven standard levels. The tower stands on the Ris0 Peninsula 0.5 Km from Roskilde Fjord. Signals from tower instrumentation are carried by cable to a meteorological station 50m downwind of the tower where both analog and digital recording equipment are housed. During the course of the experiments winds blew essentially from the west off the fjord. Data were not collected unless the wind was from off the water. The Ris^ Peninsula is 6Km north of the ancient Danish town of Roskilde which in turn is 30Km approximately southeast of Copenhagen on the island of Sjaelland. 2 . Equipment a. Meteorological Tower Arrangement Mean wind speed and direction, temperature and humidity were measured at 7, 23, 39, 56, 72 and 96m (Figure 3) . Sonic anemometer measurements were made at 21 I III m "pnmu/j|Y 1. Gate-house and fire station 2. Administration 3. Accelerator Department 4. Agricultural Department 5. Workshop 6. Physics Department 7. Electronics Department 8. Reactor Physics Department 9. Chemistry Department 10. Lecture Hull 11. Canteen 12. Library 13. Health Physics Department 14. Engineering Department and drawing offices 15. Helium plant 16. Service and maintenance 17 Research Reactor DR 1 IS. Waste treatment plant 19. Metallurgy Department 20. Hot Cells 21. Research Reactor DR 3 22. Meteorology station 23. 24. 25. 27. 28. 29. 30. 31. Isotope Laboratory Research Reactor DR 2 Reactor Engineering Department Tandem Accelerator Department of the Niels Hohr Institute Kindergarten Guest-house Staff duellings "Svaleholm" farmhouse "Djsk.ergard" farmhouse Figure 3. Ris^ Research Establishment 22 2, 23 and 72m. Fine structure turbulence measurements were made at different heights during the course of the experiment. In general, Naval Postgraduate School (NPS) equipment was deployed at 2m, 7m or 23m. Oregon State University (OSU) equipment was always at 23m. University of California, San Diego (UCSD) equipment was placed very near the top of the mast at 123m. Danish Atomic Energy Commission (AEK) equipment was located at 2m. Each group deployed sensors for measuring turbulent temperature and velocity fluctuations. The main purpose of the experiment was to make simultaneous measurements of atmospheric temperature fluctuations by different systems, at the same level and at different levels. The temperature sensor in each case was a platinum wire. The diameter of the NPS wire was 0.25 urn, of OSU 0.625 ym and of UCSD both 0.25 and 0.625 urn. By making these simultaneous measurements with similar sensors but different electronics, it was hoped (1) to find in what way they differed and (2) more importantly, to resolve some of the discrepancies surround ing the value of the scalar constant K ' . The main comparisons made in this thesis are between the NPS and OSU systems. b. NPS Platinum Resistance Thermometer At the 2m height the sensor was mounted in an aluminum holder which could hold as many as four such sensors. For the data discussed in this thesis the 23 temperature sensor was placed 5mm below a Disa hot wire anemometer. The other two positions were left vacant. At 7m the same aluminum holder was used but a Thermosys terns probe was used for the hot wire. This probe was vertically aligned and then rotated to be within 5mm to the side of the temperature sensor. A somewhat similar arrangement was made at 23m except it was more difficult to get the temperature probe close to the hot wire probe. There was a separation of approximately 1cm. c. Hot Wire Anemometer A variety of hot wire anemometers was used. They were Disa (AEK, UCSD) , Thermosys terns (NPS, OSU) , and a new wind-vane probe system (AEK) designed by Larsen and Busch (1974) . Disa probes were mounted in the aluminum holder previously described whereas the other systems had indi- vidual clamps. 3 . Recording Systems NPS, OSU and UCSD used analog tape recorders. AEK recorded digitally on magnetic tape. The NPS data analyzed for this thesis were recorded on an Ampex FR 1300 tape recorder at 7 1/2 ips using FM electronics. At this speed the 3dB point is at 2.5KHz. Each NPS temperature signal was recorded both direct and differentiated (with respect to time) . The object of the differentiation is 24 to increase the level of the signal at high frequencies above the noise level. The differentiator circuit had a gain of 6dB/octave over the differentiating band of frequencies. This band could be varied from DC to 500Hz, 1000Hz, 1500Hz, 2000Hz or 3000Hz. The frequency at which unity gain occurred could also be varied. Beyond the band of differentiation, the circuit rolled off at 6dB/octave. No other filtering of the signals was done. NPS hot wire signals were recorded directly without filtering or differentiation. The input level of the tape recorder was set to handle 1 volt rms signals. 25 IV. ANALYSIS PROCEDURES A. SELECTION OF DATA Generally when concerned with the analysis of high frequency turbulent temperature and velocity signals, it is not necessary to examine long sections of data. It was determined, however, in the preliminary analysis of this data that in order to obtain characteristic spectra, it would be necessary to extend the record length to 10 minutes. This was due to varying levels of the recorded signals, necessitating the utilization of a broadband amplifier to maintain the signal level at an almost constant level. The primary considerations for selecting a section of data for analysis were first that the temperature and velocity fluctuations be considered typical of the record and secondly, if possible, correspond to sections that were being analyzed at Oregon State University for future com- parison of results (Figure 4) . By trying to adhere to these considerations, the following data sections were analyzed: a 10 minute length of record from Run 5 commenc- ing at 1537 local Ris$ time on 30 August 1974, and a 10 minute length of record from Run 6 commencing at 1657 on 30 August 1974 (Table I) . 26 Figure 4. Example of Data Selected for Analysis 27 w ►J < Q W to < CO 2: o i— i H CJ W CO o 2: H CO nil O o Pi m o * NO Oi CO to to LO \o o ■p rt rt nd T) o O ^ •z 28 B. ANALOG EQUIPMENT AND PROCEDURES The analog analysis scheme consisted of utilizing the following state-of-the-art equipment to obtain spectra of the selected sections (Figure 5) : A Honeywell Model Ninety-Six Magnetic Tape Recorder/ Reproducer System was used to playback the recorded signals. This device is capable of recording/reproducing any combination of multi-channel direct (analog) and FM data at nine selectable servo-controlled tape speeds from 15/16 through 240 inches per second (ips) . Its standard magnetic assemblies are IRIG compatible. It is characterized by a tape speed accuracy of 0.11 and a bandwidth of 0-2.5KHz (within ldB) at a signal-to-noise ratio of 50dB when operated at 7-1/2 ips. The playback signals from the reproducing system were fed to a Preston 8300 XWB Amplifier with a bandwidth of lOOKHz and selectable gains of 1, 2, 5, 10, 20 and 50. The output from the amplifier was fed into the input of a Federal Scientific UA-500 Ubiquitous Spectrum Analyzer The selected analysis range was 0-2KHz at a sample rate of 6000hz. The analyzer has a 3dB bandwidth of 6hz and a frequency accuracy of ±0.21 of the full analysis range. The input signal to the analyzer was monitored by a Hewlett-Packard 3400A RMS Responding Voltmeter and a Tecktronix Type 502A Dual-Beam Oscilloscope. 29 l/> K U) »- Ui 2 -« Q £ O >- QI > X O u Ul Of ac 2 D OS Ul in M >■ u. u -J _j Ul < Q. Q- z 2 tO < < c - >- Ul < OL _J o u >■ X Q. to • tu a. 2 Ul i— to D < 1/1 ►- >- to 4> 6 (£) was determined, e was estimated by choosing values of (f) from the best straight line in the frequency region in which a -5/3 form was observed and then substituting into Eq. 13. A value of 0.5 was assumed for the constant K' based on results presented by Boston (1970) and Williams (1974) . c. Direct Method The kinetic energy dissipation rate was estimated directly by summing of the frequency range 33 120 100 Height 80 60 - 40 - O Run 5 A Run 6 A 20 A o Ao A o 4 5 6 U (m/sec) Figure 6. Wind Profiles Runs 5 and 6 34 from 10Hz to 2KHz the scales contributing to viscous dissi- pation according to Eq. 14. Table II summarizes the results obtained from these three methods. All values of e determined by the three methods were felt to be representative of the actual value. Therefore an average value for each run at a given height was utilized in the further analysis of the temperature spectrum. 2 . Normalization of Spectral Results a. Velocity Spectra The velocity spectra were normalized according to Eq. 3 so that a comparison could be made between dif- ferent runs and previous experiments. Figures 7 and 8 are normalized velocity spectra from Runs 5 and 6 at the 2m height. These figures show that the spectra nearly overlap with a characteristic break from the -5/3 region near log k/k = -1. b. Energy Dissipation Spectra The energy dissipation spectra were normalized according to Eq. 4. A linear plot was used to display results (Figure 9) . Maximum dissipation occurred near the value of k/k = 0.1 which is in agreement with previous research [Boston, 1970] . 35 CO CT> T-i r-- CM to vO CO oo o t-^ C7> to CM to ■«* CM vO Pi 10 CD t^- LO VO .—1 00 M3 «tf o CM !-H LO O -<* t-t lo to to CM w CO W .-4 < > CO PL. o o CO t— I Pi < P-, o CO o to 6 o CM *fr vO LO CM vO to OO OO «* rH LO rH «* *5»" to to CM "St OO o en ^- o to ^t LO vo co r-^ OO CM vO to ^t rt 6 CM 6 to CM 6 CM r-- to CM LO p! Pi 36 -e- r-H 7> O ►J 2 - 0 - -1 - -2 - -3 0 Log1() k/ks Figure 7. Normalized NPS Velocity Spectrum Run 5 at 2m 37 -e- bo o *1 0 - -1 - -2 - -3 -3 -2 Log1Q k/ks Figure 8. Normalized NPS Velocity Spectrum Run 6 at 2 in 38 ^t- f-^ .— i M / — i V 1 LO ■e- P> U) CSJ ;L" .1 " 8 k/k Figure 9. Normalized Energy Dissipation Spectrum 39 B. TEMPERATURE SPECTRUM RESULTS 1. Calculations of eQ efl values were estimated from Eq . 16 and the results are included in Table III. 2. Calculations of K ' The values of K ' were determined from Eq. 15. Values of $fi(f) were chosen from the best straight line in the frequency region in which a -5/3 form was observed. The value of e used was the average value for a given run at a particular height. Since e enters into Eq.. 15 to the -1/3 power, errors in estimating z do not seriously affect The results of the KQ * calculations are shown in Table III. An average value of 0.88 was obtained which is in quite good agreement with 0.81 by Boston (1970). It was noted that although no inherent differences in tempera- ture spectral shape were observed between OSU and NPS sensor results, the values of K ' determined at the 23m height from the OSU sensors were very near the values reported by Williams (1974) at OSU. 3 . Normalization of Spectral Results a. Temperature Spectra The temperature spectra were normalized according to Eq. 8. The temperature spectra from each run at each height were normalized and plotted (Figures 10-15). A composite spectrum was obtained by superimposing 40 tn M i — \ \ > CD -e- CD o -J 1 - -1 - -2 - -3 -1 0 Log10 k/ks Figure 10. Normalized NPS Temperature Spectrum Run 5 at 2 m 41 to V) i — \ V I CD -e- CD bO O 0 - -1 - -1 Log1Q k/k Figure 11. Normalized NPS Temperature Spectrum Run 6 at 2it m 42 ro to CD ■e- o 3 - 1 - -2 - -1 Log1Q k/ks 0 Figure 12. Normalized NPS Temperature Spectrum Run 5 at 7 m 43 N"> t/) M CD -e- CD O Log1Q k/k. Figure 13. Normalized NPS Temperature Spectrum Run 6 at 7m 44 to CO v I CD -e- CD to o rH o ►J 2 - 1 - 0 - 1 - -2 - -2 0 Log10 k/ks Figure 14. Normalized OSU Temperature Spectrum Run 5 at 23m 45 K) i — \ CD •e- CD O rH o 1 - 0 - -1 - -2 - -3 I -2 Figure 15. Log10 k/ks Normalized OSU Temperature Spectrum Run 6 at 23m 46 CD r^ vO o O vO 00 o o> K) vO vO t~- "St co r-~ CO O t^- CO cr> CO w -J < E-i CD < H CO O < < CJ CO < o I— ( CO CD o CM CD -e- eg oo o o o o o o < CD LO I o LO vO LO LO CM LO I o <5t cr> vo en o LO I o 00 vO vO LO O LO LO LO vO en vo vo Q i W o LO r-» 6 CM 6 6 to CM £ s 6 CM t-» to CM LO VO P! 47 all the spectra on a single plot (Figure 16) . The break from the -5/3 region occurs just beyond log k/k = -1. These spectra show the shape of the one-dimensional temperature spectra in air beyond the -5/3 region v/hich was one of the primary objectives of this thesis. The slope of the spectrum beyond the -5/3 break tended to be -32/5 which agrees well with Heisenberg (1948) who demon- strated that a slope of -7 should exist for very large values of k. With the exception of the temperature spectra at 2m, there is very little scatter in the data at high wave numbers . Figure 17 is a composite plot of characteristic temperature and velocity spectra. It is noted that there is very little difference between the two spectra but the temperature spectrum extends to slightly higher wave numbers than the velocity spectrum. A -32/5 slope is observed for both temperature and velocity, b. Temperature Dissipation Spectra The temperature dissipation spectra were normalized according to Eq. 9 and again plotted linearly. Figure 18 shows a typical normalized temperature dissipa- tion spectrum. There is very little difference between the temperature and velocity dissipation spectra. The normalized shapes are almost identical with the temperature spectrum dropping off slightly faster than the velocity spectrum. 48 to to / — \ N > CD •e- CD bO O -3 3 - 2 - 0 — — ■— ■"- — - — ' — ' ™ *A . ' o O^ A 2m ©^ O 7m, 23m ^A (A ^A m %> O °A# A Gb o o AA o oo A R A 09 V o , 6> ^ o 0 A . -3 -1 Log1Q k/ks 0 Figure 16. Composite Normalized Temperature Spectra 49 ro in r — \ CD -e- CD Cl) t>0 O ►J ■e- LO O ►J -2 -3 A© A° A Vel O Temp Ao -2 A© Ao A A A o A A Q t 0 Log1Q k/ks Figure 17. Comparison of Normalized Temperature and Velocity Spectra 50 3 - in CD -e- CD Cl) 0 .2 .4 k/k 8 Figure 18. Normalized Temperature Dissipation Spectrum 51 VI. SUMMARY AND CONCLUSIONS The two primary objectives of this research were to determine the shape of the high wave number one-dimensional temperature spectrum and the evaluation of the Kolmogorov scalar constant K ' . As seen in the results section, this investigator has determined that the high wave number one-dimensional temperature spectrum falls off with a slope of -32/5 beyond the -5/3 break which occurs slightly beyond log k/k = -1. Also the determination of the Kolmogorov scalar constant, Kfi ' , to be 0.88 is considered to be significant not only in absolute value but also that it increases the data base of high frequency temperature fluctuation analysis. Further, the criticism that previous evaluations were based on records that were too short is removed. It was also observed (Table III) that. K ' increased in value both with height and Reynolds Number. As an additional result of this research, it is con- cluded that the spectra of temperature and velocity at high wave numbers are very similar with the temperature spectra extending to slightly higher wave numbers than the velocity spectra but that they both fall off at the same rate. 52 BIBLIOGRAPHY Batchelor, G. K., "Small Scale Variations of Convected Quantities Like Temperature in a Turbulent Fluid (Part 1)." J. Fluid Mech. 5, p. 113-133, 1959. Batchelor, G. K., Howells, J. D., and Townsend, A. A., "Small Scale Variations of Convected Quantities Like Temperature in a Turbulent Fluid (Part 2)." J. Fluid Mech. 5, p. 134-139, 1959. Boston, N. E. J., An Investigation of High Wave Number Temperature and Velocity Spectra in Air, Ph.D. Thesis , University of British Columbia, 1970 . Corrsin, S., "On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence." J . Appl . Phys . 22, p. 469, 1951. Naval Postgraduate School Technical Report NPS-588Bb 72021, A High Frequency Platinum Thermometer System for Measuring Turbulent Atmospheric Temperature Fluctuations, by N. W. J~. Boston and E. IT. Sipe, 19 75. Gibson, C. H. , and Schwarz, H. W. , "The Universal Equilibrium Spectra of Turbulent Velocity and Scalar Fields." J. Fluid Mech. 16, p. 365-384, 1963. Heisenberg, W. Z., Physik, 124, 628, 1948. Lumley, J. L., and Panofsky, H. A., The Structure of Atmospheric Turbulence, Wiley, 1964 . Nye, J. 0., and Brodkey, R. S., "The Scalar Spectrum in the Viscous-Convective Subrange." J. Fluid Mech. 29, p. 151-163, 1967. Panofsky, H. A., "The Spectrum of Temperature." Radio Science, 4, p. 1143-1146, 1969. Stewart, R. W. , Wilson, J. R. , and Burling, R. W. , "Some Statistical Properties of Small Scale Turbulence in an Atmospheric Boundary Layer." J. Fluid Mech. 41, Part 1. p. 141-152, 1970. Williams, R. W., Jr., High Frequency Temperature and Velocity Fluctuations in the Atmospheric Boundary Layer, Ph.D. Thesis , Oregon State University, Corvallis, 1974. 53 Wyngaard, J. C, "The Effect of Velocity Sensitivity on Temperature Derivative Statistics in Isotropic Turbulence." J. Fluid Mech. 48, p. 763-769, 1971. 54 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Documentation Center 2 Cameron Station Alexandria, Virginia 22314 2. Library, Code 0212 2 Naval Postgraduate School Monterey, California 93940 3. Department Chairman, Code 58 3 Department of Oceanography Naval Postgraduate School Monterey, California 93940 4. Assoc Professor N. E. J. Boston, Code 58 Bb 1 Department of Oceanography Naval Postgraduate School Monterey, California 93940 5. Assoc Professor T. M. Houlihan, Code 59 Hm 1 Department of Mechanical Engineering Naval Postgraduate School Monterey, California 93940 6. Commanding Officer 1 Fleet Numerical Weather Central Monterey, California 93940 7. Commanding Officer 1 Environmental Prediction Research Facility ■ Monterey, California 93940 8. Department of the Navy 1 Commander Oceanographic System, Pacific Box 139 0 FPO San Francisco 96610 9. Oceanographer of the Navy 1 Hoffman II 200 Stovall Street Alexandria, Virginia 22332 10. Office of Naval Research 1 Code 480 Arlington, Virginia 22217 55 11. Dr. Robert E. Stevenson Scientific Liaison Office, ONR Scripps Institution of Oceanography La Jolla, California 92037 12. Library, Code 3330 Naval Oceanographic Office Washington, D. C. 20373 13. SIO Library University of California, San Diego P. 0. Box 2367 La Jolla, California 92037 14. Department of Oceanography Library University of Washington Seattle, Washington 98105 15. Department of Oceanography Library Oregon State University Corvallis, Oregon 97331 16. Dr. Carl Gibson University of California, San Diego Department of Ames P. 0. Box 109 La Jolla, California 92037 17. Dr. James J. O'Brien Program Director Physical Oceanography Ocean Science and Technology Division Office of Naval Research Arlington, Virginia 22217 18. Dr. R. M. Williams Oregon State University School of Oceanography Corvallis, Oregon 97331 19. Dr. J. Wyngaard AFCRL (LYB) L. G. Hanscom Field Bedford, Massachusetts 01730 20. LT Robert Thomas Simril, USN 2321 Wensley Drive Charlotte, North Carolina 28210 56 21. Dr. R. w. Burling Institute of Oceanography University of British Columbia Vancouver 8, British Columbia Canada 22. Dr. Michel Coantic Institut de Mecanique Statistique de la Turbulence 12, Avenue General Leclerc Marseille (3e) , France 23. Dr. A. Gyr Institute of Hydromechanics and Water Resources Management 8006 Zurich, Tannens trasse 1 Switzerland 24. Dr. Sjrfren Larson Research Establishment Risrf DK-4000 Roskilde, Denmark 57 Thesis j dL S517 S imri 1 c.l High frequency tem- perature fluctuations in the atmospheric boundary layer. Thesis .32 S517 S imri 1 c.l High frequency tem- pera tv re f l"ct"ations in the atmospheric boundary layer. thesS517 H!^lTle™ltemP™™ fluctuations fl'f'l'lll1'!!' I'lll Illl Illl -««ll Hill lllll ill 3 2768 001 91435 1 DUDLEY KNOX LIBRARY r I ^m ■ ■ ■Mid m