On the scaling of turbulence over an irregular rough surface in a transitionally rough regime

In this paper, the characteristics of a transitionally rough turbulent flow over a real rough surface are examined. In our research, high-resolution large eddy simulations over a scanned marine painted rough surface were carried out, and the friction Reynolds number and roughness Reynolds number (inner-scaled roughness height) were systematically varied. Away from the rough surface, the mean velocity and Reynolds stresses are unaffected by the mean roughness height. Further, the similarity away from the rough surface is clearly confirmed when we use the effective wall-normal distance. The effective wall-normal distance is defined as the wall-normal integral of the plane-porosity (void fraction). Moreover, near the rough surface, the Reynolds stresses asymptotically decay toward the bottom of the rough surface when plotted against the inner-scaled effective distance. The profiles of the mean velocity and Reynolds stresses against the effective distance reveal that the mean velocity profile can be characterized by the roughness Reynolds number (inner-scaled roughness length scale). However, the other parameters should be considered when characterizing the near-wall Reynolds stress behavior. When the budget terms in the plane and Reynolds averaged momentum equations are analyzed, it is found that the drag force term dominates the momentum transfer in the vicinity of the bottom of the rough surface. As the roughness Reynolds number increases, the pressure drag contribution to the skin friction coefficient increases, while the viscous contribution decreases.