Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

Andrew Majda; Xiaoming Wang

doi:10.1017/CBO9780511616778

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.

'… 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.'

Source: Mathematical Reviews

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Contents

Frontmatter
pp i-iv
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Contents
pp v-x
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Preface
pp xi-xii
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1 - Barotropic geophysical flows and two-dimensional fluid flows: elementary introduction
pp 1-58
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2 - The response to large-scale forcing
pp 59-79
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3 - The selective decay principle for basic geophysical flows
pp 80-114
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4 - Non-linear stability of steady geophysical flows
pp 115-137
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5 - Topographic mean flow interaction, non-linear instability, and chaotic dynamics
pp 138-182
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6 - Introduction to information theory and empirical statistical theory
pp 183-218
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7 - Equilibrium statistical mechanics for systems of ordinary differential equations
pp 219-255
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8 - Statistical mechanics for the truncated quasi-geostrophic equations
pp 256-288
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9 - Empirical statistical theories for most probable states
pp 289-316
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10 - Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview
pp 317-327
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11 - Predictions and comparison of equilibrium statistical theories
pp 328-360
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12 - Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
pp 361-410
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13 - Predicting the jets and spots on Jupiter by equilibrium statistical mechanics
pp 411-426
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14 - The statistical relevance of additional conserved quantities for truncated geophysical flows
pp 427-451
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15 - A mathematical framework for quantifying predictability utilizing relative entropy
pp 452-481
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16 - Barotropic quasi-geostrophic equations on the sphere
pp 482-549
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Index
pp 550-551
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Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

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Contents

Frontmatter
pp i-iv

Contents
pp v-x

Preface
pp xi-xii

1 - Barotropic geophysical flows and two-dimensional fluid flows: elementary introduction
pp 1-58

2 - The response to large-scale forcing
pp 59-79

3 - The selective decay principle for basic geophysical flows
pp 80-114

4 - Non-linear stability of steady geophysical flows
pp 115-137

5 - Topographic mean flow interaction, non-linear instability, and chaotic dynamics
pp 138-182

6 - Introduction to information theory and empirical statistical theory
pp 183-218

7 - Equilibrium statistical mechanics for systems of ordinary differential equations
pp 219-255

8 - Statistical mechanics for the truncated quasi-geostrophic equations
pp 256-288

9 - Empirical statistical theories for most probable states
pp 289-316

10 - Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview
pp 317-327

11 - Predictions and comparison of equilibrium statistical theories
pp 328-360

12 - Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
pp 361-410

13 - Predicting the jets and spots on Jupiter by equilibrium statistical mechanics
pp 411-426

14 - The statistical relevance of additional conserved quantities for truncated geophysical flows
pp 427-451

15 - A mathematical framework for quantifying predictability utilizing relative entropy
pp 452-481

16 - Barotropic quasi-geostrophic equations on the sphere
pp 482-549

Index
pp 550-551

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