301 pages, 24 b/w illustrations
Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions, published in 2006, 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, The Equations of Oceanic Motions will serve as both a comprehensive text and an essential reference.
"The book will surely become a standard reference for the ocean dynamicist who wants to get the equations and usual approximations right. For me, the book is already worth the price just for its thorough treatment of the Boussinesq approximation. [...] On many topics, The Equations of Oceanic Motions supplements or surpasses these standard books. It [...] deserves to become a trusted guide to the basic formulation of physical oceanography."
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
A. Equilibrium thermodynamics
B. Vector and tensor analysis
C. Orthogonal curvilinear coordinate systems
D. Kinematics of fluid motions
E. Kinematics of waves
F. Conventional and notation
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Peter Müller is a Professor of Oceanography in the School of Ocean and Earth Science and Technology at the University of Hawaii.