Geophysical Fluid Dynamics

The content of this book is based, largely, on the core curriculum in geophysƯ 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 exhaustƯ 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.

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 -…