564 pages, 150 b/w illustrations, 10 tables
The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot.
Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.
1. Barotropic geophysical flows and two-dimensional fluid flows: an elementary introduction
2. The Response to large scale forcing
3. The selective decay principle for basic geophysical flows
4. Nonlinear stability of steady geophysical flows
5. Topographic mean-flow interaction, nonlinear instability, and chaotic dynamics
6. Introduction to empirical statistical theory
7. Equilibrium statistical mechanics for systems of ordinary differential equations
8. Statistical mechanics for the truncated quasi-geostrophic equations
9. Empirical statistical theories for most probable states
10. Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview
11. Predictions and comparison of equilibrium statistical theories
12. Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
13. Predicting the jets and spots on Jupiter by equilibrium statistical mechanics
14. Statistically relevant and irrelevant conserved quantities for truncated quasi-geostrophic flow and the Burger-Hopf model
15. A mathematical framework for quantifying predictability utilizing relative entropy
16. Barotropic quasi-geostrophic equations on the sphere
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Andrew J. Majda is the Morse Professor of Arts and Sciences at the Courant Institute of New York University. Xiaoming Wang is an Associate Professor in the Department of Mathematics at Iowa State University.