The lid‐driven cavity revisited: Stability of two‐dimensional flow

The lid-driven cavity has been studied quite extensively both experimentally and numerically. Today it is the most wide-spread benchmark problem in CFD. Despite this fact, the linear stability of the steady two-dimensional flow has hardly been considered, not even for the square cavity. In the present study we revisit this classical problem and calculate the linear stability of the two-dimensional flow with respect to three-dimensional perturbations for various aspect ratios. The structure of the critical modes as well as the instability mechanism are addressed.