Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows
1st Edition
Published on 18. April 2006
978-0-511-16654-9 (ISBN)
Description
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.
Reviews / Votes
'... 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.' Mathematical ReviewsMore details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
10 Tables, unspecified; 150 Line drawings, unspecified
File size
9,84 MB
ISBN-13
978-0-511-16654-9 (9780511166549)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Andrew Majda | Xiaoming Wang
Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows
Book
05/2006
Cambridge University Press
€163.50
Shipment within 15-20 days
Persons
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.
Content
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.
