Self-sustained oscillations and vortex shedding in backward-facing step flows: Simulation and linear instability analysis

Linear instability analysis was performed to investigate the origin of the self-sustained oscillations, at St=O(0.1), which have been widely reported in backward-facing step flows. Parametric studies, based on local stability analysis of a family of time-average velocity profiles modeling those observed in recirculating flows, show that the frequency of the absolute mode is determined primarily by the shear layer thickness, and the growth rate of the absolute mode is controlled by the amount of backflow. Given the known streamwise variation of the local velocity profile in the actual flow, this implies that the oscillations are likely to be generated at the middle of the recirculation zone, where the backflow is sufficiently strong, and shear layer thickness is comparable to the step height. The corresponding frequency is determined to be St=O(0.1), because the shear layer thickness is bounded by the step height. To verify this hypothesis, mean velocity profiles obtained from a two-dimensional numerical simulation of a backward-facing step flow at Reynolds number of 3700 and expansion ratio 2:3, were analyzed to obtain the dominant absolute mode frequency, and the corresponding linear global mode was constructed by connecting local solutions at the same frequency. The frequency of the linear global mode closely matches the dominant peak frequency observed in the numerical simulation, and the mode shape showed strong resemblance to that of the dominant eddy identified in the simulation that was obtained using proper orthogonal decomposition analysis of the simulation data.