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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.Read more
- First book combining nonlinear dynamical and statistical approaches at elementary level
- Only basic prerequisites; many topics introduced through examples as and when required
- Many applications to geophysics including Great Red Spot of Jupiter
Reviews & endorsements
"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
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- Date Published: May 2006
- format: Hardback
- isbn: 9780521834414
- length: 564 pages
- dimensions: 253 x 180 x 30 mm
- weight: 1.253kg
- contains: 150 b/w illus. 10 tables
- availability: Available
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
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