Secondary instability of roughness-induced transient growth

Abstract

Calculations are performed to analyze the stability of steady roughness-induced transient growth to unsteady fluctuations. The basic states consist of an optimal transient growth model and a previously computed direct numerical simulation that fully resolves the three-dimensional roughness element. It is shown that sub-optimal transient growth produced by surface roughness is much more susceptible to destabilization than optimal perturbation predictions. The factors contributing to this behavior are analyzed in detail. Scaling properties from experiments allow computation of stability bounds for realistic surface roughness. These results are also used to explain the critical behavior seen in transition behind three-dimensional roughness elements.