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）
出版时间：2015年版
内容简介
《非线性动力学和统计理论在地球物理流动中的应用》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。
目次：正压地球物理流和二维流体流；对大尺度强迫的响应；基本地球物理流的选择性衰退原理；稳定地球流的非线性稳定性；地形流相互作用、非线性不稳定性和混沌动力学；信息理论和经验统计理论；常微分方程系统的平衡统计力学；截尾准地转方程的统计力学；最概然态的经验统计理论；地球物理流用的平衡统计理论的势应用性评估；平衡态统计理论的预测和比较；平衡态统计理论和强迫和耗散流的动力模型；平衡态统计力学预测Jupiter上的喷射流和斑点；截尾地球物理流用的额外守恒量的统计相关；应用相关熵量化可预测性的数学框架；球面上的正压准地转方程。
读者对象：流体力学以及地球物理流体相关专业的学生、老师和相关的科研人员。
目录
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 :
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 The statistical relevance of additional conserved quantities for truncated geophysical flows
15 A mathematical framework for quantifying predictability utilizing relative entropy
16 Barotropic quasi-geostrophic equations on the sphere
Index
