Impact of Spanwise Rotation on Flow Separation and Recovery Behind a Bulge in Channel Flows

Abstract: Direct numerical simulations of spanwise-rotating turbulent channel flow with a parabolic bump on the bottom wall are employed to investigate the effects of rotation on flow separation. Four rotation rates of $Ro_b := 2\Omega H/U_b = \pm 0.42, \; \pm 1.0$ are compared with the non-rotating scenario. The mild adverse pressure gradient induced by the lee side of the bump allows for a variable pressure-induced separation. The separation region is reduced (increased) when the bump is on the anti-cyclonic (cyclonic) side of the channel, compared with the non-rotating separation. The total drag is reduced in all rotating cases. Through several mechanisms, rotation alters the onset of separation, reattachment, and wake recovery. The mean momentum deficit is found to be the key. A physical interpretation of the ratio between the system rotation and mean shear vorticity, $S:=\Omega/\Omega_s$, provides the mechanisms regarding stability thresholds of $S=-0.5$ and $-1$. The rotation effects are explained accordingly with reference to the dynamics of several flow structures. For anti-cyclonic separation, particularly, the interaction between the Taylor-G\"ortler vortices and hairpin vortices of wall-bounded turbulence is proven to be responsible for the breakdown of the separating shear layer. A generalized argument is made regarding the essential role of near-wall deceleration and resultant ejection of enhanced hairpin vortices in destabilizing an anti-cyclonic flow. This mechanism is anticipated to have broad impacts on other applications in analogy to rotating shear flows, such as thermal convection and boundary layers over concave walls.