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 R e τ / (k ¯ + S) n is defined by combining the Reynolds number R e τ 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 R e τ, 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 R e τ and k ¯ + S.