SCALING OF ROUGH-WALL TURBULENCE IN A TRANSITIONALLY ROUGH REGIME

Abstract

Direct numerical simulations (DNSs) were performed for a turbulent channel flow over three-dimensional sinusoidal rough walls to test a roughness scaling method in a transitionally rough regime. Three groups of rough cases were employed to assess the scaling formula by systematically varying the friction Reynolds number Reτ and the ratio of the roughness height k to the channel half-height δ, and their predictions were compared with Nikuradse's experimental data and other roughness types. A new coupling scale Reτ/(k¯+S)n is then proposed by combining Reτ and in a logarithmic form, where n is the scaling exponent, k¯+ is the viscous-scaled mean roughness height and S is the roughness steepness. All the simulated data for the roughness function and the peak of the streamwise turbulent velocity fluctuations collapse into single curves with this coupling scale. Our investigation of the rough-wall scaling behavior with DNS data can serve as a basis for supplementing Moody's data in the transitionally rough regime.