Reynolds number dependence of double-averaged stresses in a rough-walled turbulent channel flow

Direct numerical simulations (DNS) of incompressible turbulent channel flow with irregular, three-dimensional rough walls have been performed at four friction Reynolds numbers, namely, Re=(180,240,360,540). An identical roughness topography was used for each simulation which was synthesised to have a near-Gaussian height distribution, an isotropic exponential autocorrelation function and a fixed mean peak-to-valley height. The principal interest here is to investigate the statistical response of the near-wall flow to systematic increases in the friction Reynolds number. We compare the relative magnitude of “form-induced” dispersive stresses and Reynolds stresses and show that the former tends to dominate the near-wall region as the friction Reynolds number is increased. On the other hand, the dispersive stresses become negligible in the outer flow and the turbulent stresses satisfy Townsend’s outer-layer similarity hypothesis in this region. In addition, we assess the validity of Boussinesq’s hypothesis by quantifying the alignment between the Reynolds stress and mean strain tensors using Schmitt’s Indicator Function (Schmitt, Comptes Rendus Mécanique 2007; 335:617–627). The alignment (or lack thereof) between the dispersive stress and mean strain tensors will also be discussed.