Introduction to PDEs and waves for the atmosphere and ocean

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Introduction to PDEs and waves for the atmosphere and ocean / Andrew Majda

資料種別:: 図書
出版情報:: New York : Courant Institute of Mathematical Sciences, New York University
Providence, R.I : American Mathematical Society, 2003
形態:: ix, 234 p. ; 26 cm
シリーズ名:: Courant lecture notes in mathematics ; 9 <BA42224256>
著者名:: Majda, Andrew, 1949- <DA01224251>
ISBN:: 9780821829547 [0821829548] (: pbk.)
書誌ID:: BA61234111

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注記:

Includes bibliographical references
Originally published: New York : Courant Institute of Mathematical Sciences, New York University, c2003

主題:

Atmosphere--Mathematical models; Differential equations, Nonlinear; Differential equations, Partial; Oceanography--Mathematical models; Stratified flow; Waves

言語:

英語

目次情報:

Preface

Introduction / Chapter 1.：

Basic Properties of the Equations with Rotation and Stratification / 1.1.：

Two-Dimensional Exact Solutions / 1.2.：

Buoyancy and Stratification / 1.3.：

Jet Flows with Rotation and Stratification / 1.4.：

From Vertical Stratification to Shallow Water / 1.5.：

Some Remarkable Features of Stratified Flow / Chapter 2.：

Energy Principle / 2.1.：

Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis / 2.2.：

Use of Theorem 2.4: Exact Two-Dimensional Solutions / 2.3.：

Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves / 2.4.：

Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves / 2.5.：

More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves / 2.6.：

Linear and Nonlinear Instability of Stratified Flows with Strong Stratification / Chapter 3.：

Boussinesq Equations and Vorticity Stream Formulation / 3.1.：

Nonlinear Instability of Stratified Flows / 3.2.：

Shear Flows / 3.3.：

Some Background Facts on ODEs / 3.4.：

Rotating Shallow Water Theory / Chapter 4.：

Rotating Shallow Water Equations / 4.1.：

Conservation of Potential Vorticity / 4.2.：

Nonlinear Conservation of Energy / 4.3.：

Linear Theory for the Rotating Shallow Water Equations / 4.4.：

Nondimensional Form of the Rotating Shallow Water Equations / 4.5.：

Derivation of the Quasi-Geostrophic Equations / 4.6.：

The Quasi-Geostrophic Equations as a Singular PDE Limit / 4.7.：

The Model Rotating Shallow Water Equations / 4.8.：

Preliminary Mathematical Considerations / 4.9.：

Regorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations / 4.10.：

Proof of the Convergence Theorem / 4.11.：

Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples / Chapter 5.：

Linear Wave Midlatitude Planetary Equations / 5.1.：

Dispersive Waves: General Properties / 5.2.：

Interpretation of Group Velocity / 5.3.：

Distant Propagation from a Localized Source / 5.4.：

WKB Methods for Linear Dispersive Waves / 5.5.：

Beyond Caustics: Eikonal Equation Revisited / 5.6.：

Weakly Nonlinear WKB for Perturbations Around a Constant State / 5.7.：

Nonlinear WKB and the Boussinesq Equations / 5.8.：

Simplified Equations for the Dynamics of Strongly Stratified Flow / Chapter 6.：

Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow / 6.1.：

The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow / 6.2.：

Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments / 6.3.：

The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations / Chapter 7.：

The Rotating Boussinesq Equations / 7.1.：

The Nondimensional Rotating Boussinesq Equations / 7.3.：

Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers / 7.4.：

Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations / 7.5.：

Introduction to Averaging over Fast Waves for Geophysical Flows / 7.6.：

Motivation for Fast-Wave Averaging / 8.1.：

A General Framework for Averaging over Fast Waves / 8.3.：

Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics / 8.4.：

The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit / 8.5.：

The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations / 8.6.：

Waves and PDEs for the Equatorial Atmosphere and Ocean / Chapter 9.：

Introduction to Equatorial Waves for Rotating Shallow Water / 9.1.：

The Equatorial Primitive Equations / 9.2.：

The Nonlinear Equatorial Long-Wave Equations / 9.3.：

A Simple Model for the Steady Circulation of the Equatorial Atmosphere / 9.4.：

Bibliography

Preface

Introduction / Chapter 1.：

Basic Properties of the Equations with Rotation and Stratification / 1.1.：

Two-Dimensional Exact Solutions / 1.2.：

Buoyancy and Stratification / 1.3.：

Jet Flows with Rotation and Stratification / 1.4.：

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