Amplitude-dependent stability of boundary-layer flow with a strongly non-linear critical layer

It is pointed out that the stability properties of boundary layers and channel flows depend significantly on the amplitude of the unsteady disturbance introduced, if that disturbance is not sufficiently small. This is especially so when the Reynolds number is large. The present investigation is mainly concerned with the amplitude-dependent stability of an accelerated boundary layer (on a plane wall) subjected to a small fundamental disturbance. Conditions are studied theoretically for large Reynolds numbers when the disturbance size is sufficiently large to provoke a strongly nonlinear critical layer within the flow field. Although the conducted analysis concentrates on boundary-layer flows, the analysis is broadly applicable to plane Poiseuille flow as well. It concerns the upper branch of the amplitude-dependent neutral curve,wherein the critical layer remains distinct from the wall layers, as opposed to the lower-branch stability problem of amplitude dependence studied by Smith (1979).