Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

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Mai 2006



Geophysical fluid dynamics illustrates the rich interplay between mathematical analysis, nonlinear dynamics, statistical theories, qualitative models and numerical simulations. This introduction is designed for a multi-disciplinary audience ranging from beginning graduate students to senior researchers. 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. It is the first book following this approach and contains many recent ideas and results.


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.


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.


'... 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 Reviews
EAN: 9780521834414
ISBN: 0521834414
Untertitel: 150 b/w illus. 10 tables. Sprache: Englisch.
Verlag: Cambridge University Press
Erscheinungsdatum: Mai 2006
Seitenanzahl: 564 Seiten
Format: gebunden
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