The transmission of spatially-compact internal wave packets through a critical level

Results are presented from numerical simulations of the incidence of a spat ially-compact beam of internal waves on a shear layer containing a critical level. It is found that a significant fraction of the energy of the incide nt beam is transmitted across the critical level when the packet is narrow in physical space and when the energy density of the packet is not too high so that nonlinear effects are weak. As either the packet width or its ener gy density increases, the presence of a critical level renders the shear la yer increasingly opaque to the transmission of energy. The familiar exponen tially small value of the transmission coefficient is recovered as the spat ial width of the packet exceeds (roughly) eight to ten wave lengths. (C) 19 98 Elsevier Science B.V. All rights reserved.