Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

by Andrew Majda , Xiaoming Wang

• ISBN13: 9780521834414
• ISBN10: 0521834414
• Format: Hardcover
• Copyright: 2006-05-29
• Publisher: Cambridge University Press

Summary

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 this book, 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. The book 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.

Table of Contents

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

Bibliography

Index.