The content of this book is based, largely, on the core curriculum in geophys ical fluid dynamics which I and my colleagues in the Department of Geophysical Sciences at The University of Chicago have taught for the past decade. Our purpose in developing a core curriculum was to provide to advanced undergraduates and entering graduate students a coherent and systematic introduction to the theory of geophysical fluid dynamics. The curriculum and the outline of this book were devised to form a sequence of courses of roughly one and a half academic years (five academic quarters) in length. The goal of the sequence is to help the student rapidly advance to the point where independent study and research are practical expectations. It quickly became apparent that several topics (e. g. , some aspects of potential theory) usually thought of as forming the foundations of a fluid-dynamics curriculum were merely classical rather than essential and could be, however sadly, dispensed with for our purposes. At the same time, the diversity of interests of our students is so great that no curriculum can truly be exhaust ive in such a curriculum period. It seems to me that the best that can be achieved as a compromise is a systematic introduction to some important segment of the total scope of geophysical fluid dynamics which is illustrative of its most fruitful methods.
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ISBN-13
978-1-4684-0071-7 (9781468400717)
DOI
10.1007/978-1-4684-0071-7
Schweitzer Klassifikation
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 Inviscid 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 Poincaré 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.- 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.- 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: ? = 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 Interaction Theorems.- 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 ?? L/r0< 1; the Sverdrup Relation.- 6.20 Geostrophic Approximation ? ? 1, L/r0 = O(1).- 6.21 The Thermocline Problem.- 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.- 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.
