Direct numerical simulation of a turbulent plane Couette flow over a rod-roughened wall

Abstract

A direct numerical simulation of a turbulent plane Couette flow over a two-dimensional (2D) rod-roughened wall is conducted to examine the effect of surface roughness on this type of flow. The turbulent Couette flow is driven by imposing a constant velocity on the top wall, with transverse 2D rods periodically arranged in the streamwise direction on only the stationary bottom wall. The roughness height (k) and width (w) employed are 0.2h (h is the channel-half height) and the streamwise spacing between the roughness elements (p) is set to p/k = 10. A comparison of the root-mean-square of the streamwise velocity fluctuations (u'rms) and mean Reynolds shear stress ((u'v')) between smooth- and roughwall Couette flows (hereafter, SCF and RCF) shows that the turbulence activity in the outer layer for the RCF decreases compared to that of the SCF due to the abatement of the large-scale negative u' component, indicating that the wall-similarity hypothesis between the SCF and RCF in the outer layer is not established. The weakening of the large-scale negative u' component in the outer layer results from the reduced streamwise coherence of the large-scale u' structure in the outer layer with the decreased energy. In addition, linear estimates for conditional structures demonstrate that the reduced coherence of the large-scale u' structure with less energy in the outer layer for the RCF is found to occur due to the suppressed development of a hairpin packet resulting from the weakened roll-cell motions with less influence on the near-wall region.