Spatio-temporal dynamics of a periodically driven cavity flow

Abstract

The flow in a rectangular cavity driven by the sinusoidal motion of the floor in its own plane has been studied both experimentally and computationally over a broad range of parameters. The stability limits of the time-periodic two-dimensional base state are of primary interest in the present study, as it is within these limits that the flow can be used as a viable surface viscometer (as outlined theoretically in Lopez & Hirsa 2001). Three flow regimes have been found experimentally in the parameter space considered: an essentially two-dimensional time-periodic flow, a time-periodic three-dimensional flow with a cellular structure in the spanwise direction, and a three-dimensional irregular (in both space and time) flow. The system poses a space–time symmetry that consists of a reflection about the vertical mid-plane together with a half-period translation in time (RT symmetry); the two-dimensional base state is invariant to this symmetry. Computations of the two-dimensional Navier–Stokes equations agree with experimentally measured velocity and vorticity to within experimental uncertainty in parameter regimes where the flow is essentially uniform in the spanwise direction, indicating that in this cavity with large spanwise aspect ratio, endwall effects are small and localized for these cases. Two classes of flows have been investigated, one with a rigid no-slip top and the other with a free surface. The basic states of these two cases are quite similar, but the free-surface case breaks RT symmetry at lower forcing amplitudes, and the structure of the three-dimensional states also differs significantly between the two classes.