- 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)
- - 作者：(美)马伊达
  - 出版社：世界图书出版公司
  - ISBN：9787510086281
  - 出版日期：2015/01/01
  - 页数：551
- 售价：51.6

内容大纲
作者介绍
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
  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

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目