The Effect of Modulated Driving on Non-rotating and Rotating Turbulent Plane Couette Flow

Direct numerical simulations of turbulent non-rotating and rotating Plane Couette Flow with a periodically modulated plate velocity are conducted to study the effect of modulated forcing on turbulent shear flows. The time averaged shear Reynolds number is fixed to $Re_S = 3 \cdot 10^4$, which results in a frictional Reynolds number of approximately $Re_τ\approx 400$. The modulating frequency is varied in the range $Wo\in(20,200)$, while the modulating amplitude is kept fixed at $10\%$ of the shear velocity except to demonstrate that varying this parameter changes little. The resulting shear at the plates are found to be independent of the forcing frequency, and equal to the non-modulated baseline. For the non-rotating simulations, two clear flow regions can be seen: a near wall region that follows Stokes' theoretical solution, and a bulk region that behaves similar to Stokes' solutions but with an increased effective viscosity. For high driving frequencies, the amplitude response follows the scaling laws for modulated turbulence of von der Heydt \emph{et al.} (Physical Review E 67, 046308 (2003)). Cyclonic rotation is not found to modify the system's behaviour in a substantial way, but anti-cyclonic rotation significantly changes the system's response to periodic forcing. We find that the persistent axial inhomogeneities introduced by mild anti-cyclonic rotation make it impossible to measure the propagation of the modulation adequately, while stronger anti-cyclonic rotation creates regions where the modulation travels instantaneously.