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.: |