Nonlinear Nonlocal Instability Analyses of Transitional Separation Bubbles

Kurzfassung

The linear and nonlinear instability properties of steady laminar two-dimensional incompressible boundary-layer flows with thin separation bubbles are analyzed by means of nonlocal instability theory based on the parabolized stability equations (PSE). The results are compared to data from a direct numerical simulation (DNS). Good to excellent agreement is found in the linear as well as the moderately nonlinear regime, clearly demonstrating that PSE methods are an appropriate instability analysis tool for this type of flow as well. Moreover, a vortex-shedding Strouhal number available in literature and reportedly being independent of Reynolds number and pressure gradient is verified. This Strouhal number, obtained by time-accurate Navier-Stokes simulations, is in line with the Strouhal numbers of the most amplified two-dimensional disturbances obtained from the instability analysis of the two laminar separated flows considered here.