On the equilibration of asymmetric barotropic instability

The conjunction of turbulence, waves and zonal jets in geophysical flows gives rise to the formation of potential vorticity staircases and to the sharpening of jets by eddies. The effect of eddies on jet structure, however, is fundamentally different if the eddies arise from barotropic rather than from baroclinic instability. As is well known, barotropic instability may occur on zonal jets when there is a reversal of potential vorticity gradients at the jet flanks. In this article we focus on the nonlinear stages of this instability and its eventual saturation. We consider an idealized initial state consisting of an anticyclonic potential vorticity strip sitting in the flanks of an eastward jet. This asymmetric configuration, a generalization of the Rayleigh problem, is one of the simplest barotropic jet configurations which incorporates many fundamental aspects of real flows, including linear instability and its equilibration, nonlinear interactions, scale cascades, vortex dynamics, and jet sharpening. We make use of the simplicity of the problem to conduct an extensive parameter sweep, and develop a theory relating the properties of the equilibrated flow to the initial flow state by considering the marginal stability limit, together with conservation of circulation and wave activity.