The nonlinear stability of flows over compliant walls

The weakly nonlinear, high-Reynolds-number triple-deck theory of Smith (1979) is applied to Blasius flow over a compliant wall. Attention is concentrated on Tollmien–Schlichting (TS) disturbance waves. We consider wall models of the Carpenter–Garrad type, modified to cater for three-dimensional disturbances, and allowing for the effects of nonlinear wall curvature. Supercritical equilibrium-amplitude states are possible for TS waves in a rigid-wall boundary layer, as is well known (see for example Smith 1979; Hall & Smith 1984). It is found that judicious choice of wall parameters can dramatically alter the nonlinear stability properties of TS waves in the boundary layer over a compliant wall: waves that are linearly damped may become nonlinearly unstable. Excellent agreement is obtained with rigid-wall results of Hall & Smith (1984).