Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

Andrew J Majda, Xiaoming Wang

552 pages, parution le 30/04/2006

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Résumé

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.

Sommaire

Barotropic geophysical flows and two-dimensional fluid flows: an elementary introduction
The Response to large scale forcing
The selective decay principle for basic geophysical flows
Nonlinear stability of steady geophysical flows
Topographic mean-flow interaction, nonlinear instability, and chaotic dynamics
Introduction to empirical statistical theory
Equilibrium statistical mechanics for systems of ordinary differential equations
Statistical mechanics for the truncated quasi-geostrophic equations
Empirical statistical theories for most probable states
Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview
Predictions and comparison of equilibrium statistical theories
Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
Predicting the jets and spots on Jupiter by equilibrium statistical mechanics
Statistically relevant and irrelevant conserved quantities for truncated quasi-geostrophic flow and the Burger¿Hopf model
A mathematical framework for quantifying predictability utilizing relative entropy
Barotropic quasi-geostrophic equations on the sphere
Bibliography
Index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Andrew J Majda, Xiaoming Wang
Parution	30/04/2006
Nb. de pages	552
Format	18 x 25,5
Couverture	Relié
Poids	1247g
Intérieur	Noir et Blanc
EAN13	9780521834414
ISBN13	978-0-521-83441-4