Self-sustained oscillations in separating flows: Simulation and stability analysis

Numerical simulations of a separating flow in a channel are analyzed to determine the spectral characteristics of the flow, the underlying dynamic structures and the mechanisms supporting the formation of these structures and defining their frequency. Simulations are obtained using a two-dimensional vortex-in-element code in which the velocity is determined using a higher order finite-element solution of the Poisson equation, and diffusion is simulated using random walk. Velocity spectra exhibit a Strouhal number 0(0.07) appearing at a location half way into the average recirculation zone. POD analysis of the results using a long time sample shows that the first two modes form a conjugate pair, with the same frequency 0(0.07). Linear stability analysis of the local average velocity profiles at different sections within the recirculation zone indicates the presence of an absolutely unstable mode, whose normalized frequency corresponds to 0(0.07). The shape of this mode matches well that predicted by the POD analysis.