THE VISCOUS-DIFFUSION NONLINEAR CRITICAL LAYER IN A STRATIFIED SHEAR-FLOW

Stationary finite-amplitude wave disturbances in a stratified shear flow with Richardson number larger than 1/4 are investigated for large Reynolds numbers when viscosity and thermal conductivity, as well as nonlinearity, are essential factors in the critical layer. The jumps across the critical layer in average vorticity, reflection and transmission coefficients are calculated as functions of the local Reynolds number determined by the amplitude of the incident wave. With the increase on the incident wave amplitude the asymptotic value of the Richardson number on the same side of critical layer as the incident wave tends to 1/4, the reflection coefficient tends to unity and the transmission coefficient to zero.