Analysis of the low-frequency unsteadiness of turbulent separated flows using vorticity variants

Separated flow regions often exhibit unsteadiness manifested by a low-frequency oscillation of characteristic variables. Such dynamics is often associated with an abrupt increase (or decrease) of friction drag, mixing, heat transfer, and aerodynamic noise, affecting the stability and robustness of the flow systems. Describing and predicting such events is not straightforward and dependent on heuristic and statistical approaches, lacking direct connection with the first principle from which they originate. Separated flows are inherently viscous and characterized by strong vortical motions, making vorticity a natural choice for describing their dynamics. In this study, a set of vorticity variants are investigated for several separated flows, including a turbulent wake flow behind a zero-thickness plate, a transitional supersonic flow over a backward-facing step, and a compressible turbulent boundary layer separated by an oblique impinging shock. The dynamic mode decomposition is applied to obtain the reduced-order representation of the low-frequency unsteadiness. Statistical analysis is conducted for the correlations of the vorticity variants with the integral quantities of the flows.