Direct numerical simulations of turbulent channel flows with two-and 3d superimposed sinusoidal roughness

The present work provides an analysis of turbulent channel flows with regularized wall roughness for a constant frictional Reynolds number of approximately 720 leading to a collapse in the turbulent quantities away from the wall (following Townsend’s hypothesis). The aim of this study is to investigate the effects of surface roughness on the characteristics of turbulent flows, quantify these effects, and identify relevant roughness parameters by modifying the roughness shapes previously considered in Ganju et al.¹ The effects of superimposing two roughness wavelengths as well as adding 3D effects is investigated. Three different geometry and flow configurations were analyzed: (1) a superposition of two 2D roughness profiles, (2) adding a cross-flow component in the mean flow for a 2D roughness profile, and (3) a 3D roughness profile with mean flow velocity components in streamwise and spanwise directions. Direct numerical simulations are employed with sub-Kolmogorov scale grid resolution in order to eliminate modeling assumptions and extract detailed information about the turbulent flow characteristics in the presence of roughness. In particular, the effects of wall roughness on mean velocity profiles, Reynolds stresses, as well as production and dissipation of turbulent kinetic energy are investigated.