Scaling of rough-wall turbulence in a transitionally rough regime

Abstract

In this Letter, we propose a roughness scaling method based on the direct numerical simulation of turbulent channel flow over three-dimensional sinusoidal rough walls in a transitionally rough regime. A new coupling scale Reτ/(k¯+S)n is defined by combining the Reynolds number Reτ and the roughness parameter k¯+S, where k¯+ is the mean roughness height, S is the roughness steepness, and n is the scaling exponent—which depends on the roughness type. The relationships between Reτ, k¯+S, the roughness function, the friction factor, and the peak of the streamwise turbulent velocity fluctuation are explored. This approach provides an effective way for collapsing rough-wall turbulence data with different Reτ and k¯+S.