Contributions to pressure drag in rough-wall turbulent flows: Insights from force partitioning

The force partitioning method [Menon and Mittal, J. Fluid Mech. 918, R3 (2021)] is employed to decompose and analyze the pressure-induced drag for turbulent flow over rough walls. The pressure drag force imposed by the rotation-dominated vortical regions (Q > 0, where Q is the second invariant of the velocity gradient tensor) and straindominated regions (Q < 0) are quantified using a geometry dependent auxiliary potential field (denoted by phi). The analysis is performed on data from direct numerical simulations (DNSs) of turbulent channel flows, at frictional Reynolds number of Re tau = 500, with cube and sand-grain roughened bottom walls. Results from both simulations indicate that the Q-induced pressure drag is the largest contributor (more than 50%) to the total drag on the rough walls. Data are further analyzed to quantify the effects of time-mean (coherent) and incoherent turbulent flow on the Q-induced drag force, and to discuss possible effects of roller and U-shaped structures expected to occur at the crest and midcrest locations of the roughness elements, respectively. Based on the observation that the phi field encodes information about the surface geometry that directly impacts the drag, we provide initial evidence that it can also be used to parametrize the surface drag. Specifically, we propose and test three norms based on the phi field (two of them related to the surface-induced potential flow), and explore the characterization of the Nikuradse equivalent sand-grain height ks based on these parameters for a number of channel flows with different roughness topologies. Data are provided from a suite of DNS cases by Aghaei-Jouybari et al. [J. Fluid Mech. 912, A8 (2021)]. An empirical correlation depending on these phi-based parameters, with five empirically tuned coefficients, is shown to predict ks with average and maximum errors of 10.5 and 26 percent, respectively. The results confirm that a purely geometric quantity, the phi field, provides useful additional information that can be used in drag law formulations.