马伊达编著的《非线性动力学和统计理论在地球物理流动中的应用(英文版)》是一部讲述地球物理流运用的非线性动力系统和统计理论的入门级教程，适于流体力学相关的从研究生到高级科研人员的多个交叉学科读者群。书中的很多东西应该国内没讲过，能够很好地弥补国内物理流体力学教材稀缺。没有地球物理流、概率论、信息论和平衡态统计力学的读者，这些问题将迎刃而解，书中将这些话题和相关的背景概念都引入，并通过简单例子讲述明白。

Preface

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

 1.1 Introduction

 1.2 Some special exact solutions

 1.3 Conserved quantities

 1.4 Barotropic geophysical flows in a channel domain - an important physical model

 1.5 Variational derivatives and an optimization principle for elementary geophysical solutions

 1.6 More equations for geophysical flows

 References

2 The response to large-scale forcing

 2.1 Introduction

 2.2 Non-linear stability with Kolmogorov forcing

 2.3 Stability of flows with generalized Kolmogorov forcing

 References

3 The selective decay principle for basic geophysical flows

 3.1 Introduction

 3.2 Selective decay states and their invariance

 3.3 Mathematical formulation of the selective decay principle

 3.4 Energy-enstrophy decay

 3.5 Bounds on the Dirichlet quotient, A(t)

 3.6 Rigorous theory for selective decay

 3.7 Numerical experiments demonstrating facets of selective decay

 References

 A.1 Stronger controls on A(t)

 A.2 The proof of the mathematical form of the selective decay principle in the presence of the beta-plane effect

4 Non-linear stability of steady geophysical flows

 4.1 Introduction

 4.2 Stability of simple steady states

 4.3 Stability for more general steady states

 4.4 Non-linear stability of zonal flows on the beta-plane

 4.5 Variational characterization of the steady states

 References

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

 5.1 Introduction

 5.2 Systems with layered topography

 5.3 Integrable behavior

 5.4 A limit regime with chaotic solutions

 5.5 Numerical experiments

 References

 Appendix 1

 Appendix 2

6 Introduction to information theory and empirical statistical theory

 6.1 Introduction

 6.2 Information theory and Shannon's entropy

 6.3 Most probable states with prior distribution

 6.4 Entropy for continuous measures on the line

 6.5 Maximum entropy principle for continuous fields

 6.6 An application of the maximum entropy principle to geophysical flows with topography

 6.7 Application of the maximum entropy principle to geophysical flows with topography and mean flow

 References

7 Equilibrium statistical mechanics for systems of ordinary differential equations

 7.1 Introduction

 7.2 Introduction to statistical mechanics for ODEs

 7.3 Statistical mechanics for the truncated Burgers-Hopf equations

 7.4 The Lorenz 96 model

 References

8 Statistical mechanics for the truncated quasi-geostrophic equations

 8.1 Introduction

 8.2 The finite-dimensional truncated quasi-geostrophic equations

 8.3 The statistical predictions for the truncated systems

 8.4 Numerical evidence supporting the statistical prediction

 8.5 The pseudo-energy and equilibrium statistical mechanics for

 fluctuations about the mean

 8.6 The continuum limit

 8.7 The role of statistically relevant and irrelevant

 conserved quantities

 References

 Appendix 1

9 Empirical statistical theories for most probable states

 9.1 Introduction

 9.2 Empirical statistical theories with a few constraints

 9.3 The mean field statistical theory for point vortices

 9.4 Empirical statistical theories with infinitely many constraints

 9.5 Non-linear stability for the most probable mean fields

 References

10 Assessing the potential applicability of equilibrium statistical

 theories for geophysical flows: an overview

 10.1 Introduction

 10.2 Basic issues regarding equilibrium statistical theories

 for geophysical flows

 10.3 The central role of equilibrium statistical theories with a

 judicious prior distribution and a few external constraints

 10.4 The role of forcing and dissipation

 10.5 Is there a complete statistical mechanics theory for ESTMC

 and ESTP?

 References

11 Predictions and comparison of equilibrium statistical theories

 11.1 Introduction

 11.2 Predictions of the statistical theory with a judicious prior and a

 few external constraints for beta-plane channel flow

 11.3 Statistical sharpness of statistical theories with few constraints

 11.4 The limit of many-constraint theory (ESTMC) with small

 amplitude potential vorticity

 References

12 Equilibrium statistical theories and dynamical modeling of

 flows with forcing and dissipation

 12.1 Introduction

 12.2 Meta-stability of equilibrium statistical structures with

 dissipation and small-scale forcing

 12.3 Crude closure for two-dimensional flows

 12.4 Remarks on the mathematical justifications of crude closure

 References

13 Predicting the jets and spots on Jupiter by equilibrium

 statistical mechanics

 13.1 Introduction

 13.2 The quasi-geostrophic model for interpreting observations

 and predictions for the weather layer of Jupiter

 13.3 The ESTP with physically motivated prior distribution

 13.4 Equilibrium statistical predictions for the jets and spots

 on Jupiter

 References

14 The statistical relevance of additional conserved quantities for

 truncated geophysical flows

 14.1 Introduction

 14.2 A numerical laboratory for the role of higher-order invariants

 14.3 Comparison with equilibrium statistical predictions

 with a judicious prior

 14.4 Statistically relevant conserved quantities for the

 truncated Burgers-Hopf equation

 References

 A.1 Spectral truncations of quasi-geostrophic flow with additional

 conserved quantities

15 A mathematical framework for quantifying predictability

 utilizing relative entropy

 15.1 Ensemble prediction and relative entropy as a measure of

 predictability

 15.2 Quantifying predictability for a Gaussian

 prior distribution

 15.3 Non-Gaussian ensemble predictions in the Lorenz 96 model

 15.4 Information content beyond the climatology in ensemble

 predictions for the truncated Burgers-Hopf model

 15.5 Further developments in ensemble predictions and

 information theory

 References

16 Barotropie quasi-geostrophic equations on the sphere

 16.1 Introduction

 16.2 Exact solutions, conserved quantities, and non-linear stability

 16.3 The response to large-scale forcing

 16.4 Selective decay on the sphere

 16.5 Energy enstrophy statistical theory on the unit sphere

 16.6 Statistical theories with a few constraints and statistical theories

 with many constraints on the unit sphere

 References

 Appendix 1

 Appendix 2

Index