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

Abstract

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 analyses of this phenomenon have dealt with spatially periodic, monochromatic waves. These studies observed that in the initial linear stages, the disturbance is absorbed at the critical layer and as a consequence a discontinuity in the wave-induced Reynolds stress occurs across the critical layer. Subsequently, the linear theory breaks down and nonlinear phenomena such as wave breaking and reflection result. For a more realistic representation of wave activities in the atmosphere, we employ a forcing in the form of a spatially-localized wave packet rather than a monochromatic wave, and solve the nonlinear equations numerically using Fourier transform methods and a high order compact finite difference scheme. It is found that the spatial localization delays the onset of the nonlinear breakdown in the critical layer and that there is an outward flux of momentum in the zonal direction.