Three-Dimensional Linear Stability Analysis of Cavity Flows

Numerical Simulations of the two- and three-dimensional linearized Navier–Stokes equations are performed to investigate instabilities of open cavity flows that are homogeneous in the spanwise direction. First, the onset of two-dimensional cavity instability is characterized over a range of Mach numbers, Reynolds numbers and cavity aspect ratios. The resulting oscillations are consistent with the typical Rossiter flow/acoustic resonant modes. We then identify the presence of three-dimensional instabilities of the two-dimensional basic flow and study their dependence on the parameter space. In general, the most amplified three-dimensional mode has a spanwise wavelength scaling with the cavity depth, and a frequency typically an order-of-magnitude smaller than two-dimensional Rossiter modes. The instability appears to arise from a generic centrifugal instability mechanism associated with a large vortex in the two-dimensional basic flow that occupies the downstream portion within the cavity.