The Equations of Oceanic Motions

The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small-scale motions and turbulence. Müller derives approximate equations for all oceanic motions, emphasizing the assumptions made. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. This comprehensive textbook provides the basic theoretical background for graduate students and researchers of physical oceanography.

Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large-scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, Müller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

Preface; 1. Introduction; 2. Equilibrium thermodynamics of sea water; 3. Balance equations; 4. Molecular flux laws; 5. The gravitational potential; 6. The basic equations; 7. Dynamical impact of the equation state; 8. Free wave solution on a sphere; 9. Asymptotic expansions; 10. Reynolds decomposition; 11. Boussinesq approximation; 12. Large scale motions; 13. Primitive equations; 14. Representations of vertical structure; 15. Ekman layers; 16. Planetary geostrophic flows; 17. Tidal equations; 18. Medium scale motions; 19. Quasi-geostrophic flows; 20. Motions on the f-plane; 21. Small scale motions; 22. Sound waves; Appendix A. Equilibrium thermodynamics; Appendix B. Vector and tensor analysis; Appendix C. Orthogonal curvilinear coordinate systems; Appendix D. Kinematics of fluid motions; Appendix E. Kinematics of waves; Appendix F. Conventional and notation; References; Index.

This comprehensive 2006 textbook derives and classifies the most common dynamic equations used in physical oceanography, emphasizing the assumptions made and the physical processes eliminated. Providing a clear exposition of the concepts for graduate students and researchers of physical oceanography, all of the necessary mathematical tools are covered in appendices.