Amplitudedependent stability of boundarylayer flow with a strongly nonlinear critical layer
Abstract
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 amplitudedependent 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 boundarylayer flows, the analysis is broadly applicable to plane Poiseuille flow as well. It concerns the upper branch of the amplitudedependent neutral curve,wherein the critical layer remains distinct from the wall layers, as opposed to the lowerbranch stability problem of amplitude dependence studied by Smith (1979).
 Publication:

IMA Journal of Applied Mathematics
 Pub Date:
 January 1983
 Bibcode:
 1983JApMa..30....1B
 Keywords:

 Boundary Layer Stability;
 Critical Flow;
 Flow Theory;
 High Reynolds Number;
 Traveling Waves;
 Wall Flow;
 Amplitudes;
 Flow Velocity;
 Laminar Flow;
 Nonlinear Equations;
 Phase Shift;
 Pressure Oscillations;
 Propagation Modes;
 Rayleigh Equations;
 Reversed Flow;
 Suction;
 Vorticity Equations;
 Fluid Mechanics and Heat Transfer