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Waves and flows are pervasive on and within Earth. This book presents a unified physical and mathematical approach to waves and flows in the atmosphere, oceans, rivers, volcanoes and the mantle, emphasizing the common physical principles and mathematical methods that apply to a variety of phenomena and disciplines. It is organized into seven parts: introductory material; kinematics, dynamics and rheology; waves in non-rotating fluids; waves in rotating fluids; non-rotating flows; rotating flows; and silicate flows. The chapters are supplemented by 47 'fundaments', containing knowledge that is fundamental to the material presented in the main text, organized into seven appendices: mathematics; dimensions and units; kinematics; dynamics; thermodynamics; waves; and flows. This book is an ideal reference for graduate students and researchers seeking an introduction to the mathematics of waves and flows in the Earth system, and will serve as a supplementary textbook for a number of courses in geophysical fluid dynamics.
List of contents
Preface; Part I. Introductory Material: 1. Introduction; 2. Getting started; Part II. Kinematics, Dynamics and Rheology: 3. Kinematics of deformation and flow; 4. Dynamics and the stress tensor; 5. Some thermodynamics; 6. Shear rheology; 7. Static state and perturbations; 8. Introduction to rotating fluids; Part III. Waves in Non-Rotating Fluids: 9. Introduction to waves; 10. Elastic waves; 11. Deep-water waves; 12. Linear shallow-water waves; 13. Non-linear shallow-water waves; 14. Other non-rotating waves; Part IV. Waves in Rotating Fluids: 15. Geostrophic, inertial and rossby waves; 16. Rotationally modified waves; 17. Equatorial waves; 18. Coastal and topographic waves; Part V. Non-Rotating Flows: 19. Orientation to one-dimensional flow; 20. Steady channel flow; 21. Unsteady channel flow: hydraulic shock waves; 22. Gravitationally forced flows; 23. A simple model of turbulent flow; 24. Some simple turbulent flows; Part VI. Flows in Rotating Fluids: 25. Ekman layers; 26. Atmospheric flows; 27. Oceanic currents; 28. Vortices; Part VII. Silicate Flows: 29. Equations governing silicate flows; 30. Cooling the Earth; 31. Cooling the mantle; 32. Cooling the core; 33. Overview of volcanic flows; 34. Flow in volcanic conduits; 35. Lava flow; Part VIII. Fundaments: Appendix A. Mathematics; Appendix B. Dimensions and units; Appendix C. Kinematics; Appendix D. Dynamics; Appendix E. Thermodynamics; Appendix F. Waves; Appendix G. Flows; References; Index.
About the author
David E. Loper is an Emeritus Professor at Florida State University. After completing his Ph.D. in Mechanical Engineering, and after a brief stint in the aerospace industry and a postdoctoral appointment at the National Center for Atmospheric Research (NCAR), Professor Loper took a joint position in Applied Mathematics and the Geophysical Fluid Dynamics Institute at Florida State University, where he is a Distinguished Research Professor. Later in his career, his departmental affiliation changed to Geology. He was a co-founder and secretary of SEDI (Study of the Earth's Deep Interior, a Committee of the International Union of Geodesy and Geophysics) and is Fellow of the American Geophysical Union.
Summary
This book presents a unified physical and mathematical approach to waves and flows in the atmosphere, oceans, rivers, volcanoes and the mantle. Covering various topics including kinematics, dynamics and rheology, rotating and non-rotating flows, it is an ideal reference for graduate students and researchers.
Report
'At last! An applied mathematician who ably explains complicated geophysical phenomena thoroughly and transparently. Read, enjoy and learn! I have.' Paul Roberts, University of California, Los Angeles
