Nonlinear evolution of Rayleigh waves in an initial value context: Non-symmetric input and cross-flow

In recent papers the present authors considered the effects of small cross- flow on the evolution of two unequal oblique waves. In these studies the re lative size of the crossflow meant that a diffusion (or buffer) layer was r equired around the critical layer to smooth out the algebraic growth in the mean-flow distortion generated by the nonlinear critical-layer interaction s. The present analysis increases the cross-flow to an order of magnitude s uch that the buffer and critical layers coalesce. In this instance the nonl inear critical layer contains viscous as well as nonequilibrium effects. Th e resulting amplitude equations are solved for perturbations initiated at a fixed station in the flow.