How are flow structures related to drag forces and equivalent sandgrain height in turbulent flows over rough walls?

The Force Partitioning Method (FPM, Menon and Mittal, JFM 907, A37, 2021) is employed to dissect the hydrodynamic drag over rough walls in a turbulent channel flow. The contributions of distinct flow structures (vortices and straining regions) on the pressure drag are quantified using an auxiliary potential field (Φ), which depends solely on the roughness geometry. Four sources of drag are identified and their relative importance quantified. These are: Q-induced force (Q being the second invariant of the velocity gradient tensor), viscous momentum diffusion induced pressure force, and viscous shear force on the roughness elements and shear force on the base surface. Results indicate that the Q-induced force is the major contributing factor to pressure drag and is mainly produced by the strain-dominated, i.e. Q<0, regions upstream of each roughness element. Based on these insights, we explore characterizing the equivalent sandgrain height k_s for fully rough channel flows using information embedded in the Φ field. An empirical correlation based on several parameters that can be evaluated from  Φ is shown to predict k_s with rms and maximum errors of about 12 and 30 percent, respectively. The comparison used data from a suite of DNS cases (Jouybari et al., JFM, 912, A8, 2021).