Geophysical Fluid Dynamics II: Stratified / Rotating Fluid Dynamics of the Atmosphere―Ocean (Springer Textbooks in Earth Sciences, Geography and Environment)

✍ Scribed by Emin Özsoy

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 332
• Category: Library

✦ Synopsis

This book develops a fundamental understanding of geophysical fluid dynamics based on a mathematical description of the flows of inhomogeneous fluids. It covers these topics:

1. development of the equations of motion for an inhomogeneous fluid

2. review of thermodynamics

3. thermodynamic and kinetic energy equations

4. equations of state for the atmosphere and the ocean, salt, and moisture effects

5. concepts of potential temperature and potential density

6. Boussinesq and quasi-geostrophic approximations

7. conservation equations for vorticity, mechanical and thermal energy instability theories, internal waves, mixing, convection, double-diffusion, stratified turbulence, fronts, intrusions, gravity currents

Graduate students will be able to learn and apply the basic theory of geophysical fluid dynamics of inhomogeneous fluids on a rotating earth, including:

1. derivation of the governing equations for a stratified fluid starting from basic principles of physics

2. review of thermodynamics, equations of state, isothermal, adiabatic, isentropic changes

3. scaling of the equations, Boussinesq approximation, applied to the ocean and the atmosphere

4. examples of stratified flows at geophysical scales, steady and unsteady motions, inertia-gravity internal waves, quasi-geostrophic theory

5. vorticity and energy conservation in stratified fluids

6.boundary layer convection in stratified containers and basins

✦ Table of Contents

Preface
Contents
1 Hydro-Thermo-Dynamics of Stratified Fluids
1.1 Basic Hydrodynamics: Continuity and Momentum Equations
1.2 Thermodynamics
1.2.1 First Law of Thermodynamics
1.2.2 Mechanical and Thermal Energy Equations
1.2.3 Equilibrium Thermodynamics
1.2.4 Second Law of Thermodynamics
1.2.5 Different Forms of the Thermodynamic Equation
1.3 Thermodynamic Equations Applied to the Atmosphere and the Ocean
1.3.1 Relative Roles of Compression in the Atmosphere and the Ocean
1.3.2 Thermodynamic Equation for the Atmosphere
1.3.3 Thermodynamic Equation for the Ocean
1.4 Vorticity Dynamics
2 Basic State and Scales
2.1 Existence of a ``Basic State''
2.2 Scale Heights
2.3 Perturbation Equations
2.4 Order of Magnitude Analysis
2.5 Scale Analyses
2.6 Brunt–Väisälä (Stratification) Parameter
2.6.1 Atmosphere
2.6.2 Ocean
2.6.3 Combined Equations for the Atmosphere and Ocean
3 Quasi-geostrophic Theory
3.1 Development of Quasi-geostrophic Theory
3.2 Quasi-geostrophic, Barotropic Motions
3.2.1 Barotropic Rossby Waves
3.2.2 Barotropic Rossby Waves in Basic Zonal Flows
3.2.3 Barotropic Instability
3.3 Quasi-geostrophic, Baroclinic Motions
3.3.1 Rossby Waves in Quasi-geostrophic Stratified Fluids
3.3.2 Boussinesq Approximations
3.3.3 Physics Represented by Quasi-geostrophic Equations
3.3.4 Quasi-geostrophic Motion Linearly Superposed on Uniform Current
3.3.5 Energetics of Linear Motions Superposed on Uniform Zonal Flow
3.3.6 Interpretation of Quasi-geostrophic Energetics
3.3.7 Quasi-geostrophic Equations for Stratified Uniform Flow
3.3.8 Quasi-geostrophic Motion in Stratified Uniform Flow
3.4 Baroclinic Instability in a Uniform Zonal Current
3.4.1 Integrated Equations
3.4.2 Howard Semicircle Theorem
4 Internal Waves
4.1 Basic Equations
4.1.1 Re-Scaled Equations
4.1.2 Oscillatory Motion in Stratified Environment (N2)
4.1.3 Total Energy in a Boussinesq Fluid
4.1.4 Further Manipulation of Boussinesq Equations
4.2 Internal Gravity Waves Without the Effects of Earth's Rotation
4.2.1 A Note on 3-D Internal Waves
4.2.2 Internal Waves in the 2-D Plane
4.2.3 Refraction of Internal Gravity Waves
4.2.4 Reflection of Internal Gravity Waves on a Slope
4.3 Internal Waves Under Joint Effects of Earth's Rotation and Stratification
4.3.1 Internal Inertia-Gravity Waves
4.3.2 Horizontal Modes of Motion
4.3.3 Case 1: Poincaré Waves, κh2>k2
4.3.4 Case 2: Kelvin Waves, κ2h<k2
4.4 Inertia-Gravity Waves: Constant Stratification N2
4.4.1 Energetics of Internal Waves in a Uniformly Stratified Fluid
4.4.2 Momentum Flux in a Stratified Fluid
4.4.3 Semi-Infinite Boussinesq Fluid with Moving Sinusoidal Boundary
4.5 Internal Waves in Mean Flow
4.5.1 3D Waves in Mean Flow
4.5.2 2D Waves in Shear Flow
4.5.3 Energy Conservation in Uniform Shear Flow
4.5.4 Taylor-Goldstein Eigenvalue Equation
4.5.5 Critical Layer in a Stratified Shear Flow
4.5.6 Stability of Simple Stratified Shear Flows
4.5.7 Stability Analyses and the Howard Semi-Circle Theorem
4.5.8 Kelvin-Helmholtz Instability
5 Boundary Layers in Stratified Fluids
5.1 A Review of Boundary Layers in Homogeneous and Stratified Fluids
5.1.1 Boundary Layer Scaling
5.1.2 Boundary Layer Equations
5.1.3 Similarity Solutions
5.2 Thermal Boundary Layers
5.2.1 Equations for Inhomogeneous Boundary Layers
5.2.2 Free Convection—Homogeneous Interior Fluid
5.2.3 Free Convection with Stratified Interior (Buoyancy Layer)
5.2.4 Convection in Stratified Containers
5.2.5 Thermal Stratification in a Cylinderical Container
5.2.6 Interior and Boundary Layer Flows
5.3 Rayleigh–Bénard Thermal Convection
6 Jets and Plumes
6.1 Momentum Jets
6.1.1 Plane Laminar Jet
6.1.2 Plane Turbulent Jet
6.1.3 Axisymmetric Turbulent Jet
6.2 Plumes and Buoyant Jets
6.2.1 Simple Jet with Passive Diffusion of Concentration or Temperature
6.2.2 Pure Plume
6.2.3 Buoyant Jet
6.2.4 Axisymmetric Pure Plumes and Buoyant Jets
7 Exercises
7.1 Chapter 1摥映數爠eflinkchap111, Exercise 1
7.2 Chapter 3摥映數爠eflinkchap333, Exercise 1
7.3 Chapter 3摥映數爠eflinkchap333, Exercise 2
7.4 Chapter 4摥映數爠eflinkchap444, Exercise 1
7.5 Chapter 4摥映數爠eflinkchap444, Exercise 2
7.6 Chapter 5摥映數爠eflinkchap555, Exercise 1
7.7 Chapter 5摥映數爠eflinkchap555, Exercise 2
7.8 Chapter 5摥映數爠eflinkchap555, Exercise 3
7.9 Chapter 5摥映數爠eflinkchap555, Exercise 4
7.10 Chapter 5摥映數爠eflinkchap555, Exercise 3
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