Dynamical Models for Control of Cavity Oscillations

We investigate nonlinear dynamical models for self-sustained oscillations in the flow past a rectangular cavity. The models are based on the method of Proper Orthogonal Decomposition (POD) and Galerkin projection, and we introduce an inner product and formulation of the equations of motion which enables one to use vector-valued POD modes for compressible flows. We obtain models between 3 and 20 states, which accurately describe both the short-time and long-time dynamics. This is a substantial improvement over previous models based on scalar-valued POD modes, which capture the dynamics for short time, but deviate for long time.