Global stability of a lid-driven cavity with throughflow: Flow visualization studies

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Abstract
Flow visualization studies of a lid-driven cavity (LDC) with a small amount of throughflow reveal multiple steady states at low cavity Reynolds numbers. These results show that the well-known LDC flow, which consists of a primary eddy and secondary corner eddies, is only locally stable, becomes globally unstable, and competes with at least three other steady states before being replaced by a time-periodic flow. The small amount of throughflow present in this system seems to have no qualitative effect on the fluid flow characteristics. These observations suggest that multiple stable steady states may also exist in closed LDC’s. Since stability properties of the closed LDC flows are virtually unexplored, we interpret our flow visualization results by first proposing an expected behavior of an idealized (free-slip end walls) LDC and then treating the problem at hand as a perturbation of the ideal case. The results also suggest that there are nonunique and competing sequences of transitions that lead the flow in a LDC from laminar steady state toward turbulence.

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