Vortex dynamics and flow patterns in a two-dimensional oscillatory lid-driven rectangular cavity

Abstract

The vortex dynamics in a two-dimensional oscillatory lid-driven cavity with depth-to-width ratio 1:2 has been investigated, covering a wide range of Reynolds numbers and Stokes numbers where this flow is known to be in the two-dimensional regime. Numerical simulations show that the present flow can be divided into four flow patterns based on the vortex dynamics. The regions of these flow patterns are given in the Stokes number and Reynolds number space. For the flow pattern with lowest Reynolds number, there is no transfer of vortices between two successive oscillation half-cycles while for the three other patterns, vortices are carried over from one oscillation half-cycle to the next. For a given Stokes number, the flow pattern appears sequentially as the Reynolds number increases, showing that the transition between the different flow patterns depends strongly on the Reynolds number. However, if the frequency of oscillation is increased (i.e., the Stokes number is increased) for a given Reynolds number, the extrema of the stream function have less time to grow and the center of the primary vortex has less time to move away from the lid. To compensate these effects, the amplitude has to be increased with increasing frequency to maintain the same flow pattern.