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Imversity Mcrafihns International INFORMATION TO USERS This reproduction was made from a copy of a manuscript sent to us for publication and microfilming. While the most advanced technology has been used to pho­ tograph and reproduce this manuscript, the quality of the reproduction is heavily dependent upon the quality of the material submitted. Pages in any manuscript may have indistinct print. In all cases the best available copy has been filmed. The following explanation of techniques is provided to help clarify notations which may appear on this reproduction. 1. Manuscripts may not always be complete. When it is not possible to obtain missing pages, a note appears to indicate this. 2. When copyrighted materials are removed from the manuscript, a note ap­ pears to indicate this. 3. Oversize materials (maps, drawings, and charts) are photographed by sec­ tio n in g the o rig in al, beginning at the upper left hand com er and co n tin u ­ ing from left to right in equal sections with small overlaps. Each oversize page is also filmed as one exposure and is available, for an additional charge, as a standard 35mm slide or in black and white paper format. * 4. Most photographs reproduce acceptably on positive microfilm or micro­ fiche but lack clarity on xerographic copies made from the microfilm. For an additional charge, all photographs are available in black and white standard 35mm slide format. * "‘For more information about black and white slides or enlarged paper reproductions, please contact the Dissertations Customer Services Department. IMversity Mcrafihns International 8603031 Lorenson, Claude Pierre DYNAMICAL PROPERTIES OF SUPERFLUID TURBULENCE The Ohio State University Ph.D. 1985 University Microfilms International 300 N. Zeeb Road, Ann Arbor, Ml 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V 1. Glossy photographs or pages ______ 2. Colored illustrations, paper or print _______ 3. Photographs with dark background _____ 4. Illustrations are poor copy _______ 5. Pages with black marks, not original copy ______ 6. Print shows through as there is text on both sides of p a g e ________ 7. Indistinct, broken or small print on several pages i / ^ 8. Print exceeds margin requirements ______ 9. Tightly bound copy with print lost in spine ________ 10. Computer printout pages with indistinct print _______ 11. Page(s) ______________ lacking when material received, and not available from school or author. 12. Page(s) ______________ seem to be missing in numbering only as text follows. t3 . Two pages numbered . Text follows. 14. Curling and wrinkled pages ______ 15. Dissertation contains pages with print at a slant, filmed as received __ 16. Other _______________________________________________________________________________ University Microfilms International DYNAMICAL PROPERTIES OF SUPERFLUID TURBULENCE DISSERTATION Presented in Partial Fulfillment of the Requirement for the Degree of Doctor of Philosophy in the Graduate School of the Ohio State University By Claude Pierre Lorenson, B.S., M.S. The Ohio State University 1985 Reading Committee: Approved by James T. Tough i— C. David Andereck ' _ Advisor William F. Saam Department of Physics Supported by the National Science Foundation, Low-Temperature Physics, Grant No. DMR 8218052 ACKNOWLEDGEMENTS I would sincerely like to thank my advisor Dr. J. T. Tough. I realize that I pushed his patience to the limit throughout this research effort. The completion of this dissertation is a tribute to his creativity and patience. Every time we were stuck with a problem, Dr. Tough could always come up with a suggestion, "something to try" so that we could keep moving. I used quite a few "nicknames" for Dr. Tough throughout the years ... yet the best one is advisor, never has his advice let me down. One person who helped me a lot through this work is my friend and co-worker Donald Griswold. Without his help this work would not be completed by now. I thank him for writing most of the computer programs and also for helping in the construction of the apparatus and in the data taking. His presence in the lab made the day to day work enjoyable. I would like to thank Dr. V. U. Nayak not only for teaching me how to run the experimental apparatus but also for stressing the importance of quality in a project. Because of/my association with him I learned a lot about the basic problems of experimental low-temperature physics and how to solve them. I am grateful for all the support of the technical staff at O.S.U. during my stay. Special thanks to Bob Merritt for keeping our helium supply constant and to Bob Kindler for the great work he has done on our experimental probe. I greatly appreciate the love and support of my parents. They were always willing to help me throughout my career. I could never repay all the sacrifices made by them to help me. I thank all my friends, especially Alain Gauthier, to help making my stay in Columbus so enjoyable. Finally I would like to thank my best friend, my wife Pandora for all the love, support and understanding she has given me. This work was supported by National Science Foundation-Low Temperature Physics-Grant #DMR 8218052. VITA April 29, 1957 Born: Jonquiere, P. Quebec Canada 1980 B.S.: Universite Laval Quebec City, Canada 1980-1982 Graduate Teaching Assistant, The Ohio State University, Columbus, Ohio 1982-1985 Graduate Research Assistant, The Ohio State University Columbus, Ohio 1982 M.S.: The Ohio State University Columbus, Ohio Field of Study: Condensed Matter Physics TABLE OF CONTENTS ACKNOWLEDGEMENTS .................................................. ii VITA ................................................................ iv LIST OF TABLES .................................................... vii LIST OF FIGURES ..................................................... viii CHAPTER PAGE 1. INTRODUCTON................................................ 1 1.1 Introduction ..................................... 1 1.2 Early Theories and Tests ....................... 1 1.3 Turbulent Thermal Counterflow .................. 3 1.4 Theories and Models .............................. 7 1.5 Previous Experiments and Motivation for This Research .................................... 12 2. APPARATUS ................................................ 16 2.1 Introduction ....................... 16 2.2 Design Consideration ............................ 16 2.3 Probe Overview .................................. 17 2.4 Vacuum C a n ....................................... 20 2.5 Helium Reservoir ................................ 20 2.6 Flow Tube Assembly .............................. 25 2.7 Counterflow C e l l .................. 26 2.8 Superleaks ....................................... 28 2.9 Thermometers and Heaters ....................... 29 2.10 Pressure Transducer .............................. 32 2.11 Feedthroughs and Electrical Wiring ............ 40 2.12 Cryostat and Vacuum Systems ..................... 44 3. EXPERIMENTAL PROCEDURES ................................. 49 3.1 Introduction ..................................... 49 3.2 Temperature Measurements ....................... 49 3.3 Temperature Regulation ......................... 53 3.4 Chemical Potential Measurements ................ 58 3.5 Counterflow Experiments ......................... 61 3.6 Spectral Analysis ................................ 63 v 3.7 Relative P o w e r ................................... 66 3.8 Time Constant Experiment ........................ 67 4. EXPERIMENTAL RESULTS ................................... 73 4.1 Introduction ..................................... 73 4.2 Steady State Data in Turbulent Counterflow . 73 4.3 Power Spectra Measurements ..................... 82 4.4 Relative Power Measurements ..................... 96 4.5 Time Constant Measurements ..................... 103 4.6 Amplitude Probability Distribution ............ 106 5. DISCUSSION .............................................. 113 5.1 Introduction ..................................... 113 5.2 Observations of Fluctuations ................... 113 5.3 Amplitude of the Fluctuations and Relaxation Time at the TI/TII Transition .................. 117 5.4 Future Work ....................................... 120 APPENDICES A. Construction of Transducer ............................ 122 A.l Introduction ..................................... 122 A.2 Body Assembly ..................................... 122 A.3 Membrane Assembly ................................ 125 A.4 Closing the Transducer .......................... 128 A.5 Leak Testing ..................................... 129 B. Sensitivity T e s t ....................................... 131 B.l Introduction ..................................... 131 B.2 Physical Analysis ................................ 131 B . 3 Resonance in the Transducer ..................... 144 C.l Computer Programs ................................ 144 BIBLIOGRAPHY ....................................................... 165 vi LIST OF TABLES TABLE PAGE 1. Values of dR/dT and R for all thermometers at 1.6 ° K ................................................ 31 2. Description of Figure 1 7 .............................. 47 vii LIST OF FIGURES FIGURE PAGE 1. Schematic diagram of a counterflow apparatus .... 4 2. Cubic dependence of the dissipation ................ 6 3. Crossing vortex lines reconnecting in the Schwarz m o d e l ................................ 11 4. Vortex line density graph v.s heat current
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