A numerical simulation of the nonlinear critical layer evolution of a forced Rossby wave packet in a zonal shear flow

We investigate the nonlinear development of a forced Rossby wave packet in the presence of a critical layer in a zonal shear flow. Most previous analy ses of this phenomenon have dealt with spatially periodic, monochromatic wa ves. These studies observed that in the initial linear stages, the disturba nce is absorbed at the critical layer and as a consequence a discontinuity in the wave-induced Reynolds stress occurs across the critical layer. Subse quently, the linear theory breaks down and nonlinear phenomena such as wave breaking and reflection result. For a more realistic representation of wav e activities in the atmosphere, we employ a forcing in the form of a spatia lly-localized wave packet rather than a monochromatic wave, and solve the n onlinear equations numerically using Fourier transform methods and a high o rder compact finite difference scheme. It is found that the spatial localiz ation delays the onset of the nonlinear breakdown in the critical layer and that there is an outward flux of momentum in the zonal direction. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.