Excitation of nearly steady finite-amplitude barotropic waves.

Abstract

We obtain an exact nonlinear stationary solution for barotropic waves in a beta-plane channel and show that it can be excited under a range of initial conditions. Results show that a finite- amplitude wave in a constant shear flow, given an initial phase tilt against the shear and a sufficient initial amplitude, interacts with the mean flow to produce a nearly steady state close to the exact stationary solution. This equilibration process involves nonlinear transients; in particular, as the flow equilibrates, the emergence of critical levels is accompanied by the neutralization of local mean vorticity gradients at these levels, thus allowing the solution to attain a nonsingular modal structure. -Authors