Scaling of rough-wall turbulence in a transitionally rough regime

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 Re-tau/((k) over bar (+) S)(n) is defined by combining the Reynolds number Re-tau and the roughness parameter (k) over bar (+) S, where (k) over bar (+) 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 Re-tau, (k) over bar (+) 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 Re-tau and (k) over bar (+) S.