Geostrophic turbulence and geophysical circulations

Abstract

Basic vorticity principles give immediate insight into the behavior of turbulent flow of a classic, homogeneous fluid. Analogously, potential vorticity principles help to describe the large-scale flows of the Earth’s oceans and atmosphere, and those of the other planets; system rotation and density stratification are dominant effects. In both cases the tracer-like properties of vorticity and potential vorticity yield insight and analysis. The Ertel-Rossby potential vorticity arises essentially from Kelvin’s circulation theorem for fluid circuits lying on surfaces of constant potential density. Here we describe some of the dynamics of such fluids, notably the large-scale ‘geography’ of potential vorticity provided by the shape of the planet (or bounding container), waves that depend upon this geography, mean circulations that determine the geography, and geostrophic turbulence that actively help to shape this geography. The tracer-like property of potential vorticity encourages us to consider fluid circulations as being the product of boundary sources and sinks of potential vorticity, distributed by mean circulation and mixed (often homogenized) by geostrophic turbulence, with attendant back-effects on the mean circulation.