A Numerical Simulation of Barotropic Instability. Part II: Wave-Wave Interaction

Abstract

A fully nonlinear numerical model of the point jet barotropic instability is used to test and confirm the hypothesis that the magnitude of the wave vorticity does not exceed the magnitude of the initial sheer. This result arises directly from the local conservation of vorticity following a parcel and the fact that unstable waves are principally confined to the region where the zonal mean vorticity can be smoothed by the wave so as to eliminate the instability. Comparisons are made between fully nonlinear and quasi-linear models of the point jet instability and their tracer transport properties. Differences become particularly evident after wave saturation. The most important effect neglected by the wave-mean flow model appears to be the advection of wave vorticity by the most unstable mode. However, as equilibration of the instability proceeds, the globally averaged properties of both models are found to be similar.