图书信息
图书目录
大气与海洋的偏微分方程和波引论（影印版）
暂无简介
作者：
Andrew Majda
定价：
135.00 元
出版时间：
2025-02-13
ISBN：
978-7-04-063094-7
物料号：
63094-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
偏微分方程
重点项目：
暂无
版面字数：
400.00千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次印刷时间：
2025年
- 前辅文
- Preface
- Chapter 1. Introduction
- 1.1. Basic Properties of the Equations with Rotation and Stratification
- 1.2. Two-Dimensional Exact Solutions
- 1.3. Buoyancy and Stratification
- 1.4. Jet Flows with Rotation and Stratification
- 1.5. From Vertical Stratification to Shallow Water
- Chapter 2. Some Remarkable Features of Stratified Flow
- 2.1. Energy Principle
- 2.2. Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis
- 2.3. Use of Theorem 2.4: Exact Two-Dimensional Solutions
- 2.4. Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves
- 2.5. Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves
- 2.6. More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves
- Chapter 3. Linear and Nonlinear Instability of Stratified Flows with Strong Stratification
- 3.1. Boussinesq Equations and Vorticity Stream Formulation
- 3.2. Nonlinear Instability of Stratified Flows
- 3.3. Shear Flows
- 3.4. Some Background Facts on ODEs
- Chapter 4. Rotating Shallow Water Theory
- 4.1. Rotating Shallow Water Equations
- 4.2. Conservation of Potential Vorticity
- 4.3. Nonlinear Conservation of Energy
- 4.4. Linear Theory for the Rotating Shallow Water Equations
- 4.5. Nondimensional Form of the Rotating Shallow Water Equations
- 4.6. Derivation of the Quasi-Geostrophic Equations
- 4.7. The Quasi-Geostrophic Equations as a Singular PDE Limit
- 4.8. The Model Rotating Shallow Water Equations
- 4.9. Preliminary Mathematical Considerations
- 4.10. Rigorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations
- 4.11. Proof of the Convergence Theorem
- Chapter 5. Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples
- 5.1. Linear Wave Midlatitude Planetary Equations
- 5.2. Dispersive Waves: General Properties
- 5.3. Interpretation of Group Velocity
- 5.4. Distant Propagation from a Localized Source
- 5.5. WKB Methods for Linear Dispersive Waves
- 5.6. Beyond Caustics: Eikonal Equation Revisited
- 5.7. Weakly Nonlinear WKB for Perturbations Around a Constant State
- 5.8. Nonlinear WKB and the Boussinesq Equations
- Chapter 6. Simplified Equations for the Dynamics of Strongly Stratified Flow
- 6.1. Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow
- 6.2. The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow
- 6.3. Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments
- Chapter 7. The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations
- 7.1. Introduction
- 7.2. The Rotating Boussinesq Equations
- 7.3. The Nondimensional Rotating Boussinesq Equations
- 7.4. Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers
- 7.5. Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations
- 7.6. Preliminary Mathematical Considerations
- 7.7. Proof of the Convergence Theorem
- Chapter 8. Introduction to Averaging over Fast Waves for Geophysical Flows
- 8.1. Introduction
- 8.2. Motivation for Fast-Wave Averaging
- 8.3. A General Framework for Averaging over Fast Waves
- 8.4. Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics
- 8.5. The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit
- 8.6. The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations
- Chapter 9. Waves and PDEs for the Equatorial Atmosphere and Ocean
- 9.1. Introduction to Equatorial Waves for Rotating Shallow Water
- 9.2. The Equatorial Primitive Equations
- 9.3. The Nonlinear Equatorial Long-Wave Equations
- 9.4. A Simple Model for the Steady Circulation of the Equatorial Atmosphere
- Bibliography
