Response of a Turbulent Separation Bubble to Variations in Freestream Pressure Gradients

Separating turbulent boundary layers over a flat plate are investigated by DNS at $Re_\theta$ = 600. A suction-blowing velocity distribution is imposed at the top boundary to produce an adverse-to-favorable pressure gradient (PG), leading to a closed turbulent separation bubble. The separation bubble is found to naturally oscillate at a Strouhal number $St \equiv fL_{sep}/U_\infty \approx 0.37$. In order to gain insights into the natural time-scales of these bubbles we impose different magnitudes of the imposed PG and also varying the PG in time. Analysis of the simulation data shows that the change in the bubble size is mainly due to shear layer ``flapping" at the downstream end of the bubble. The analysis of the separating shear layer confirms its similarity to a plane mixing layer, albeit one that is formed by counter-flowing, and not co-flowing streams. Variations in the magnitude of the PG enable us to modulate the velocity ratio $R = (U_1-U_2)/(U_1+U_2)$ (subscripts denote the two sides of the mixing layer) in the separating shear layer. For some cases, the value of this critical parameter is found to exceed the convective to a global instability transition threshold in the separating shear layer.