Spatial Simulations of Oblique Transition in a Boundary Layer

Abstract

We present an investigation of oblique transition, i.e. transition initiated by a pair of oblique waves. The breakdown of oblique waves has been found to cause rapid transition in compressible boundary- (Fasel & Thumm, 1991) and shear layers (Gathmann et al., 1993) and in channel flows (Schmid & Henningson, 1992). In the channel flow study it was found that non-linearity rapidly excited streamwise vortices. By the lift-up effect the vortices generated large amplitude low and high-speed streaks in the streamwise velocity components. The oblique transition scenario involves transient growth mechanisms, which in shear flows can lead to significant energy growth of three-dimensional (’streaky’) disturbances even for subcritical Reynolds numbers. Physically, the growth is due to the lift-up mechanism. Mathematically it can be explained by the fact that the linearized Navier-Stokes operator has non-orthogonal eigenfunctions, a necessary condition for subcritical transition to occur (Henningson & Reddy, 1994).