Pulsating Turbulent Channel Flows over Sandgrain Roughness

In this work we investigate the behavior of oscillating channel turbulence over a rough surface by running a series of DNS under $Re_\tau = 1500$. The virtual sandgrain roughness used consists of closely-packed ellipsoids with random orientations. The roughness height is 4\% of the channel half height. Pulsation of the flow is applied by a sinusoidal variation of the pressure gradient around the mean value giving the target $Re_\tau$. Three frequencies in the very high, high, and intermediate regimes are examined. The time-averaged centroid of the force exerted by the roughness is the same as it is in the non-oscillating case. The equivalent roughness height remains the same for the intermediate- and low-frequency pulsation while increasing significantly for the high-frequency one. Compared with the canonical Stokes layer whose thickness is $2l_s$, the oscillation wave propagates further into the channel over the rough wall to $10l_s$. This range does not vary with the change of the oscillation frequency for the roughness-forcing combinations considered here, and it is still within the roughness sublayer ($y<3k$). The local wake flow around the roughness elements responds actively to the pulsation and leads to a significant variation in the wall stress during each cycle.