NUMERICAL STUDY OF AN INTERACTING ROSSBY WAVE AND BAROTROPIC ZONAL FLOW NEAR A CRITICAL LEVEL.

Abstract

The initial value problem of a forced Rossby wave encountering a critical level in a barotropic zonal shear flow which can change in response to the wave momentum flux divergence is studied. The main result of the calculation is that the shape of the zonal flow profile changes with time in such a way as to reduce the potential vorticity gradient to zero at the critical level. For this configuration, the wave is totally reflected at the critical level and in the absence of dissipation no longer interacts with the zonal flow. Details of the evolution toward the steady state depend on the ratio of two time scales, one a measure of the wave amplitude and the other representing the time it takes for the wave momentum flux to be concentrated in a well-defined critical layer.