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University of Cincinnati UNIVERSITY OF CINCINNATI Date:___________________ I, _________________________________________________________, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair: _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ Theoretical Analysis of the Temperature Variations and the Krassovsky Ratio for Long Period Gravity Waves A dissertation submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY (Ph.D) in the Department of Physics of the College of Arts and Science 2008 by Tharanga Manohari Kariyawasam M.S., University of Cincinnati, Cincinnati, OH B.S., University of Colombo, Colombo, Sri Lanka Committee Chair: Professor Tai-Fu Tuan i Abstract Based on the assumption that they are caused by atmospheric gravity waves rather than atmospheric tides, this study aims at developing a theoretical analysis of the long period (~ 8 hour) fluctuations of both the Meinel OH band intensity and the rotational temperature. Eddy thermal conduction and eddy viscosity is included in the calculation. In addition, to account for the very long periods (~ 8 hour), Coriolis force due to earth’s rotation will also be taken into account by employing the “shallow atmosphere” approximation. The current theoretical analysis differ from the prior models in that it will include the Coriolis force and the model will deal with very long periods, and in addition the height varying background wind is also included in the discussion. Long period fluctuations in the airglow have been measured in many recent experimental observations (Taylor M.J., Gardner L.C., Pendleton W.R., Adv. Space Res., 2001). The Krassovsky ratio which determines the efficiency of producing an intensity fluctuation for a given temperature fluctuation, and also the phase difference between the intensity and temperature fluctuation will also be calculated based on the gravity wave assumption. ii iii Acknowledgements First and foremost, I would like to convey my sincere gratitude to my faculty advisor, Professor Tai-Fu Tuan, for his invaluable guidance and relaxed, thoughtful insight in completing this work. I greatly appreciate the sincere support that he has provided me in all my endeavors over the years. I also would like to extend my deepest gratitude to my dissertation committee members Professor Paul Esposito, Professor Rostislav Serota, Professor Rohana Wijewardhana and Professor Bernie Goodman for their comments, advice and for helping me in many ways to complete my research work successfully. I am particularly thankful to Professor Frank Pinski, Dr. Richard Gass and Professor Nageswari Shanmugalingam for sharing their constructive ideas and for their help in my research project. I would also like to thank Dr M. J Taylor and Dr. J.R Winick for sharing their insight and for the helpful discussions. I am indebted to the faculty members at the Physics Department for their many advice and lessons in Physics. I am grateful to Donna Deutenberg, Elle Mengon, John Whitaker and Melody Whitlock and all other staff members at the Physics Department for their cooperation and support. I wish to thank my friends, at the Department of Physics, for the most enjoyable time and for the wonderful memories. Many thanks, to the Department of Physics and the Graduate Student Association for the financial support. A special thanks to my husband for his understanding, continuous encouragement and guidance without reservation. Finally, I wish to thank my parents for their love and guidance, without which I would never have enjoyed so many opportunities. iv TABLE OF CONTENTS Abstract……………………………………………………………………………….. i Acknowledgement……………………………………………………………………. ii Table of Contents………………………………………………………………….…. iii CHAPTERS 1 Introduction 1.1 Atmospheric Gravity waves 01 1.2 Airglow Emissions in the Middle Atmosphere 03 1.3 Krassovsky Ratio Method 07 1.4 Experimental observations 1.4.1 Taylor’s Observations 09 1.4.2 Oznovich’s Observations 11 1.5 Shallow Atmosphere Approximation 12 2 Mathematical Formulation 2.1 Basic Hydrodynamic Theory 14 2.2 Gravity wave Model 18 2.3 Atmospheric Model Used 23 2.4 Airglow Response 2.4.1 Eulerian continuity equation 26 2.4.2 The internal gravity wave response 28 2.4.3. Brightness Weighted Temperature Method 30 3 Hydroxyl Chemical Kinetic Model 3.1 Background 34 3.2 OH Vibrational Kinetic Model 36 4 Results & Discussions 4.1 Numerical Results and Discussions 43 4.2 Conclusion 50 5 Figures 52 6 Bibliography 91 7 Appendices 7.1 Appendix A 98 7.2 Appendix B 101 7.3 Appendix C 113 v CHAPTER 1 INTRODUCTION 1.1 Atmospheric Gravity Waves Low altitude tropospheric sources such as large earth quakes or nuclear explosions are capable of generating upper atmospheric modes with very long periods which are observed as Traveling Ionospheric Disturbances (TIDs). Gravity waves are these neutral atmospheric disturbances that are generated by various low altitude sources like earthquakes, artificial wave sources such as nuclear explosions and high altitude sources like hurricanes and tropospheric thunderstorms. Due to these gravity waves originated in the lower atmosphere by the weather related disturbances and/or orographic forcing, large amounts of energy and momentum are transported to the upper atmosphere. Neutral air is also known to propagate in the thermosphere by solar EUV heat input within the thermosphere. A discrete spectrum of atmospheric gravity wave modes are supported by the earth’s atmosphere and different scientists have studied disturbances caused by various gravity waves with periods ranging from a few minutes to several hours. In essence, the gravity waves generated by these different sources are capable of propagating vertically and horizontally, interact non- linearly and greatly influence the constituent densities and the energy and the momentum flows of the atmosphere. Since C. O. Hines [Hines, 1960] published his universally accepted and widely used linear gravity wave theory in 1960, extensive theoretical as well as experimental studies of the gravity waves and their effects displayed in diverse atmospheric phenomena has become a major goal of atmospheric science research. Experimentally obtained measurements of wind data using radar techniques, chemical and rocket smoke trail releases, minor constituent concentrations taken using a variety of instrumentation, temperature and temperature fluctuation measurements obtained using lidar experiments, etc are studied and analyzed by scientists in atmospheric modeling to establish density, pressure, temperature and background concentration profiles. Experimental detection of minor constituent concentrations and temperature fluctuation measurements are conducted using radar, lidar and satellite aided observational techniques. Images of the structure of gravity waves are taken using all-sky imagery. Using the observational data gathered with the aid of lidar, rockets, all-sky imagery, etc, scientists engaged in atmospheric modeling of gravity waves attempts to explain experimental data to better understand and predict the atmospheric effects. 2 1.2 Airglow Emissions in the Middle Atmosphere Throughout the middle atmosphere these gravity waves are known to be a major source of meso-scale fluctuations, especially in the mesosphere and the lower thermosphere (MLT) region, where profound impact is observed on the temperature structure and the general circulation. Early evidence of minor constituent motions is available in the form of auroral displays, wave-like patterns in the radio echoes and meteor trail distortions. At MLT heights the upward propagating atmospheric gravity waves create substantial fluctuations in the line of sight column brightness and rotational temperature of several airglow emissions by perturbing the concentration profiles of the reacting minor species whose reaction rates are also temperature dependant. When observed during daytime the airglow is called dayglow and when observed in the night it is referred to as nightglow. The airglow emissions are used extensively to study temperature and other fluctuations in the upper atmosphere and also to study the temporal and spatial variations of the concentration profiles of the reacting minor species. In studying the turbulence and the stability of the middle atmosphere it is important to factor into consideration atmospheric dynamics and chemistry because this height region is abundant of dynamical and photochemical interactions. The propagation of atmospheric gravity waves in the middle atmosphere affects the emissions of various wave lengths, produced due to decaying of atmospheric constituents. Atmospheric dynamics deals with these effects of Internal Gravity Waves (IGW) on the mesospheric airglow emissions. Atmospheric chemistry 3 is important because the propagation of the IGW changes the temperature dependant rate coefficients of chemical reactions by changing the neutral temperatures of the atmosphere and also influences the chemically active constituent concentrations. The kinetic energy densities and the temperature fluctuations can be calculated using the mesospheric airglow emissions. Since the photochemistry of the middle atmosphere is affected by the propagating atmospheric gravity waves, various scientists have used the response due to gravity
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