Introduction to Geophysical Fluid Dynamics

This second chapter offers a brief introduction to geophysical fluid dynamics—the dynamics of rotating, stratified flows. We start with the shallow water equations, which govern columnar motion in a thin layer of homogeneous fluid. Roughly speaking, the solutions of the shallow-water equations comprise two types of motion: ageostrophic motions, including inertia-gravity waves, on the one hand, and nearly geostrophic motions on the other. In rapidly rotating flow, these two types of motion may, in some sense, decouple. We seek simpler equations that describe only the nearly geostrophic motion. The simplest such equations are the quasigeostrophic equations. In the quasigcostrophic equations, potential vorticity plays the key role: The potential vorticity completely determines the velocity field that transports it, thereby controlling the whole dynamics. We begin by generalizing our previously derived fluid equations to a rotating coordinate frame.