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大气与海洋的偏微分方程和波引论（影印版）

样章
作者：
Andrew Majda
定价：
135.00 元
版面字数：
400千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2025年
ISBN：
978-7-04-063094-7
物料号：
63094-00
出版时间：
2025-02-13
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
暂无
  • 目录
    • 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

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