An Introduction to Atmospheric Gravity Waves

Acknowledgements

Dedication

Preface

Fundamentals

1.1 Introduction

1.2 Some Wave Mechanics

1.3 The Buoyant Force

1.4 The Boussinesq Approximation

Problems

The Linear Theory

2.1 Introduction

2.2 The Taylor– Goldstein Equation

2.3 A Simple Solution

2.4 The WKB or “ Slowly Varying” Method

2.5 Energetics

Problems

Mountain Waves

3.1 Introduction

3.2 Uniform Flow Over a Surface Corrugation

3.3 The Two-Dimensional Mountain

3.4 The Three-Dimensional Mountain

3.5 Nonorographic Gravity Waves

Problems

Ducted Gravity Waves

4.1 Introduction

4.2 Wave Reflection and Refraction at an Elevated Layer

4.3 Wave Trapping, Energy Flux, and Wave Resonance

4.4 Reflection at the Ground Surface

4.5 Wave Ducts

Problems

Gravity Wave Instability and Turbulence

5.1 Introduction

5.2 Parcel Exchange Analysis of Flow Stability

5.3 Wave Instability

5.4 The Critical Level

5.5 Neutral, Stable, and Unstable Modes

5.6 Wave-Modulated Richardson Number

5.7 Wave–Turbulence Coupling

5.8 Jefferys’ Roll-Wave Instability Mechanism

Problems

Wave Stress

6.1 Introduction

6.2 Mathematical Derivation

6.3 Variation of Wave Stress with Height

6.4 Mountain Wave Stress

6.5 Secondary Effects of Wave Drag

Problems

Gravity Waves in the Middle and Upper Atmosphere

1 Introduction

2 Background

3 Interia-Gravity Waves in the Middle Atmosphere

4 Planetary Waves in the Middle Atmosphere

5 Midlatitude Wave Spectra

6 Modeling the Gravity Wave Fluxes in the MUA

Problems

Wave Stress Parameterization

8.1 Introduction

8.2 Wave-Saturation Parameterization

8.3 Parameterization Methods

8.4 Saturation Limits and Other Problems

8.5 Problems

Observations and Measurements of Gravity Waves

9.1 Introduction

9.2 Ground-Based Measurements

9.3 Free-Balloon Soundings

9.4 Remote Measurements

Problems

Gravity Wave Analyses

10.1 Introduction

10.2 Analyses of Tropospheric Gravity Waves

10.3 Gravity Wave Analyses in the MUA

Problems

The Hydrostatic Atmosphere

A.1 The Hydrostatic Approximation

A.2 The Scale Height of the Isothermal Atmosphere

A.3 Adiabatic Lapse Rate

A.4 Potential Temperature

A.5 Boussinesq Relations

A.6 The Geostrophic Wind

A.7 The Critical Level

A.8 Convolution

A.9 The Eckman Wind Spiral

A.10 Numerical Methods

Bibliography

Index

IG Series