Stability balloon for the double-lid-driven cavity flow

Abstract

The linear stability of the two-dimensional, steady, incompressible flow in a rectangular cavity is investigated numerically. The flow is driven by the parallel or antiparallel motion of two facing walls. When the cavity is infinitely extended in the spanwise direction a variety of different, three-dimensional flow instabilities can arise. We provide an overview on the global structure of the critical hypersurface in the three-dimensional parameter space spanned by the cross-sectional aspect ratio and the two side-wall Reynolds numbers. It turns out that the critical hypersurface is made up of six major segments belonging to different modes of instability. The interrelation and connectivity of these critical modes is elucidated.