Eddy genesis in the double-lid-driven cavity

Abstract

Using an integral-equation method which employs the authors' new and widely-applicable technique of singularity annihilation, we investigate the eddy genesis in the benchmark problem of steady viscous flow in a lid-driven cavity, two of whose opposite edges move with different velocities. The method enables us to investigate the eddy structure in the resulting flow with confidence since the singularity-annihilation method results are demonstrated to be virtually independent of the boundary discretization, so effective is the suppression of the singularity. In the event that only one of the edges moves, we provide convincing quantitative corroboration of the geometrical symmetry of the corner eddies first predicted by Moffatt (1). When two edges move with a relative speed ratio, we present an interesting study of the genesis of a variety of topologically-distinct flows, and the way in which these metamorphose as the speed ratio is altered. Some remarkable corner-eddy flow structures are presented, and a full explanation of all observed flow structures is proffered.