Effects of surface roughness topography in transient channel flows

The dynamical effects of roughness geometry on the response of a half-height turbulent channel flow to an impulse acceleration are investigated using direct numerical simulations. Two rough surfaces different in the surface height spectrum are compared between themselves and with a smooth-wall baseline case. Both rough cases develop from a transitionally rough state to a fully rough one. Results show that on rough walls the thickness of the roughness sublayer (RSL), defined as the layer with significant form-induced stresses, stays almost constant. The ensemble-average flows inside the RSL stays close to equilibrium throughout the transient. This is shown by the form-induced perturbations largely scaling with the mean velocity at the edge of the RSL. Inside the RSL, turbulence develops rapidly to the new steady state, accompanied by substantial changes in the Reynolds stress balance. In contrast, the flow above the RSL recovers long after the sublayer is fully developed, without a significant change in Reynolds stress balance. The geometry of the roughness plays an important role in determining the rate of response of turbulence throughout the boundary layer. This work provides detailed explanation of the suppression of reverse transition by surface roughness in response to a mean flow acceleration.