Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

by Andrew Majda, Xiaoming Wang

Overview

This introduction to the important interplay between nonlinear dynamics and statistical theories for geophysical flows is designed for a multi-disciplinary audience ranging from graduate students to senior researchers. Novel applications of information theory are utilized to simplify, unify, and compare the equilibrium statistical theories. Topics and related background concepts are introduced and developed through elementary examples and discussion throughout the text as they arise. No previous background in geophysical flows is needed to read the text.

Product Details

ISBN-13:	9780521834414
Publisher:	Cambridge University Press
Publication date:	05/11/2006
Edition description:	New Edition
Pages:	564
Product dimensions:	7.09(w) x 9.96(h) x 1.18(d)

About the Author

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.

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.

Editorial Reviews

"Written with a firmly interdisciplinary perspective, this book is a valuable contribution to the fascinating intersection of applied mathematics and geophysical fluid dynamics. The authors are adept at illuminating and motivating rigorous mathematical analysis, qualitative models, and physical intuition through exceptionally lucid exposition and a rich collection of examples."
Christopher C. Hallstrom, Mathematical Reviews

From the Publisher