Quasi-geostrophic theory of oceans and atmosphere

Machine generated contents note: pt. I Fundamentals -- 1. Basic Continuum Mechanics -- 1.1. Kinematics of Continua -- 1.1.1. The Continuum Hypothesis and the Concept of Material Element -- 1.1.2. Kinematics of Material Elements -- 1.2. Dynamics of Fluids -- 1.2.1. Momentum Equation -- 1.2.2. Basic Concepts of Vorticity Dynamics -- 1.2.3.A Look at Turbulence -- 1.2.4. Appendix: Galilean Covariance of the Lagrangian Derivative -- 2. Basic Geophysical Fluid Dynamics -- 2.1. Constitutive Equations -- 2.1.1. Equations of State -- 2.1.2. Thermodynamic Equations of Dry Air and Seawater -- 2.1.3.Compressibility and Incompressibility -- 2.2. Internal Gravity Waves in Adiabatic and Frictionless Fluids -- 2.2.1. Definition of the Model -- 2.2.2. Evolution Equations for the Velocity, Pressure and Density Fields -- 2.3. Rotating Flows -- 2.3.1. Basic Parameters of the Earth and Local Cartesian Coordinate Systems -- 2.3.2. Uniformly Rotating Coordinate Frames.

Contents note continued: 2.3.3. The Equations of Fluid Mechanics for Uniformly Rotating Systems -- 2.3.4. Covariance of the Gradient Operator in Passing from an Inertial to a Rotating Frame of Reference -- 2.3.5. Governing Equations of Long Gravity Waves -- 2.3.6. Poincare and Kelvin Waves -- 2.3.7. Vorticity and Potential Vorticity of a Uniformly Rotating Flow -- 2.3.8. Appendix: Hydraulics and Earth's Rotation -- 2.4. Large-Scale Flows -- 2.4.1. Phenomenology of Large-Scale Circulation of Geophysical Flows -- 2.4.2. Governing Equations of Large-Scale, Geophysical Flows -- pt. II Applications -- 3. Quasi-Geostrophic Single-Layer Models -- 3.1. Shallow-Water Model -- 3.1.1. The Quasi-Geostrophic, Shallow-Water Model -- 3.1.2. Developments of the Shallow-Water Equations for Modelling Wind-Driven Ocean Circulation -- 3.2. Homogeneous Model -- 3.2.1. The Ekman Layers -- 3.2.2. The Homogeneous Model of the Wind-Driven Oceanic Circulation -- 3.2.3. Classical Solutions of the Homogeneous Model.

Contents note continued: 3.2.4. Basic Dynamics of the Atmospheric Ekman Layer -- 4. Quasi-Geostrophic Two-Layer Model -- 4.1. Basic QG Equations for the Two-Layer Model -- 4.1.1. The Quasi-Geostrophic Two-Layer Model -- 4.1.2. Frictional Interaction Between the Layers -- 4.1.3. The Vorticity Equations of the Two-Layer Model -- 4.1.4. Wave-Like Solution of the Model -- 4.1.5. Behaviour of the Interface -- 4.2. Energetics of the Two-Layer Model -- 4.2.1. Energetics Associated to the Quasi-Geostrophic Two-Layer Model -- 4.2.2. Available Potential Energy of a Two-Layer Fluid -- 4.2.3. Integrated Energetics of the Two-Layer Model (4.65)---(4.66) -- 5. Quasi-Geostrophic Models of Continuously Stratified Flows -- 5.1. QG Continuously Stratified Flows in the Ocean -- 5.1.1. The Quasi-Geostrophic Oceanic Mesoscale -- 5.1.2. Quasi-Geostrophic Dynamics at the Oceanic Basin Scale -- 5.1.3. The Effects of Bathymetry -- 5.1.4. Forced and Wave-Like Circulation.

Contents note continued: 5.2. QG Continuously Stratified Flows in the Atmosphere -- 5.2.1. Basic Synoptic-Scale Dynamics of the Atmosphere -- 5.2.2. Thermally Forced Stationary Waves -- 5.2.3. The Effects of Topography.

Large-scale winds and currents tend to balance Coriolis and pressure gradient forces. The time evolution of these winds and currents is the subject of the quasi-geostrophic theory. Chapter 1 presents concepts and equations of classical inertial fluid mechanics. Chapter 2 deals with the equations of thermodynamics that close the governing equations of the fluids. Then, the motion is reformulated in a uniformly rotating reference frame. Chapter 3 deals with the shallow-water model and the homogeneous model of wind-driven circulation. The chapter also describes a classical application of the Ekma --Page 4 of cover.