ALBERT

Note: Contents: 1 Preliminaries. - 1.1 Geophysical Fluid Dynamics. - 1.2 The Rossby Number. - 1.3 Density Stratification. - 1.4 The Equations of Motion in a Nonrotating Coordinate Frame. - 1.5 Rotating Coordinate Frames. - 1.6 Equations of Motion in a Rotating Coordinate Frame. - 1.7 Coriolis Acceleration and the Rossby Number. - 2 Fundamentals. - 2.1 Vorticity. - 2.2 The Circulation. - 2.3 Kelvin's Theorem. - 2.4 The Vorticity Equation. - 2.5 Potential Vorticity. - 2.6 The Thermal Wind. - 2.7 The Taylor-Proudman Theorem. - 2.8 Geostrophic Motion. - 2.9 Consequences of the Geostrophic and Hydrostatic Approximations. - 2.10 Geostrophic Degeneracy. - 3 lnviscid Shallow-Water Theory. - 3.1 Introduction. - 3.2 The Shallow-Water Model. - 3.3 The Shallow-Water Equations. - 3.4 Potential-Vorticity Conservation: Shallow-Water Theory. - 3.5 Integral Constraints. - 3.6 Small-Amplitude Motions. - 3.7 Linearized Geostrophic Motion. - 3.8 Plane Waves in a Layer of Constant Depth. - 3.9 Poincare and Kelvin Waves. - 3.10 The Rossby Wave. - 3.11 Dynamic Diagnosis of the Rossby Wave. - 3.12 Quasigeostrophic Scaling in Shallow-Water Theory. - 3.13 Steady Quasigeostrophic Motion. - 3.14 Inertial Boundary Currents. - 3.15 Quasigeostrophic Rossby Waves. - 3.16 The Mechanism for the Rossby Wave. - 3.17 The Beta-Plane. - 3.18 Rossby Waves in a Zonal Current. - 3.19 Group Velocity. - 3.20 The Method of Multiple Time Scales. - 3.21 Energy and Energy Flux in Rossby Waves. - 3.22 The Energy Propagation Diagram. - 3.23 Reflection and the Radiation Condition. - 3.24 Rossby Waves Produced by an Initial Disturbance. - 3.25 Quasigeostrophic Normal Modes in Closed Basins. - 3.26 Resonant Interactions. - 3.27 Energy and Enstrophy. - 3.28 Geostrophic Turbulence. - Appendix to Chapter 3. - 4 Friction and Viscous Flow. - 4.1 Introduction. - 4.2 Turbulent Reynolds Stresses. - 4.3 The Ekman Layer. - 4.4 The Nature of Nearly Frictionless Flow. - 4.5 Boundary-Layer Theory. - 4.6 Quasigeostrophic Dynamics in the Presence of Friction. - 4.7 Spin-Down. - 4.8 Steady Motion. - 4.9 Ekman Layer on a Sloping Surface. - 4.10 Ekman Layer on a Free Surface. - 4.11 Quasigeostrophic Potential Vorticity Equation with Friction and Topography. - 4.12 The Decay of a Rossby Wave. - 4.13 Side-Wall Friction Layers. - 4.14 The Dissipation of Ens trophy in Geostrophic Turbulence. - 5 Homogeneous Models of the Wind-Driven Oceanic Circulation. - 5.1 Introduction. - 5.2 The Homogeneous Model. - 5.3 The Sverdrup Relation. - 5.4 Meridional Boundary Layers: the Munk Layer. - 5.5 Stommel's Model: Bottom Friction Layer. - 5.6 Inertial Boundary-Layer Theory. - 5.7 Inertial Currents in the Presence of Friction. - 5.8 Rossby Waves and the Westward Intensification of the Oceanic Circulation. - 5.9 Dissipation Integrals for Steady Circulations. - 5.10 Free Inertial Modes. - 5.11 Numerical Experiments. - 5.12 Ekman Upwelling Circulations. - 5.13 The Effect of Bottom Topography. - 5.14 Concluding Remarks on the Homogeneous Model. - 6 Quasigeostrophic Motion of a Stratified Fluid on a Sphere. - 6.1 Introduction. - 6.2 The Equations of Motion in Spherical Coordinates: Scaling. - 6.3 Geostrophic Approximation: ε = O(L/r0 ) ≪ 1. - 6.4 The Concept of Static Stability. - 6.5 Quasigeostrophic Potential-Vorticity Equation for Atmospheric Synoptic Scales. - 6.6 The Ekman Layer in a Stratified Fluid. - 6.7 Boundary Conditions for the Potential-Vorticity Equation: the Atmosphere. - 6.8 Quasigeostrophic Potential-Vorticity Equation for Oceanic Synoptic Scales. - 6.9 Boundary Conditions for the Potential-Vorticity Equation: the Oceans. - 6.10 Geostrophic Energy Equation and Available Potential Energy. - 6.11 Rossby Waves in a Stratified Fluid. - 6.12 Rossby-Wave Normal Modes: the Vertical Structure Equation. - 6.13 Forced Stationary Waves in the Atmosphere. - 6.14 Wave-Zonal Flow Interactions. - 6.15 Topographic Waves in a Stratified Ocean. - 6.16 Layer Models. - 6.17 Rossby Waves in the Two-Layer Model. - 6.18 The Relationship of the Layer Models to the "Level" Models. - 6.19 Geostrophic Approximation ε ≪ L/r0 〈 1; the Sverdrup Relation. - 6.20 Geostrophic Approximation ε ≪ 1, L/r0 = O(1). - 6.21 The Thermocline Problem. - 6.22 Layer Models of the Thermocline. - 6.23 Flow in Unventilated Layers: Potential Vorticity Homogenization. - 6.24 Quasigeostrophic Approximation: an Alternative Derivation. - 7 Instability Theory. - 7.1 Introduction. - 7.2 Formulation of the Instability Problem: the Continuously Stratified Model. - 7.3 The Linear Stability Problem: Conditions for Instability. - 7.4 Normal Modes. - 7.5 Bounds on the Phase Speed and Growth Rate. - 7.6 Baroclinic Instability: the Basic Mechanism. - 7.7 Eady's Model. - 7.8 Charney's Model and Critical Layers. - 7.9 Instability in the Two-Layer Model: Formulation. - 7.10 Normal Modes in the Two-Layer Model: Necessary Conditions for Instability. - 7.11 Baroclinic Instability in the Two-Layer Model: Phillips' Model. - 7.12 Effects of Friction. - 7.13 Baroclinic Instability of Nonzonal Flows. - 7.14 Barotropic Instability. - 7.15 Instability of Currents with Horizontal and Vertical Shear. - 7.16 Nonlinear Theory of Baroclinic Instability. - 7.17 Instability of Non parallel Flow. - 8 Ageostrophic Motion. - 8.1 Anisotropic Scales. - 8.2 Continental-Shelf Waves. - 8.3 Slow Circulation of a Stratified, Dissipative Fluid. - 8.4 The Theory of Frontogenesis. - 8.5 Equatorial Waves. - Selected Bibliography. - Index.