Analysis of the different sources of stress acting in fully rough turbulent flows over geometrical roughness elements

The discrete element roughness method is considered in this article for the prediction of turbulent flows over rough walls. This approach is derived by ensemble- and volume-averaging the Navier-Stokes equations, providing double-averaged Navier-Stokes equations, and yielding three unknown terms in the momentum equation: the Reynolds stress and dispersive stress tensors and the average drag force acting on the roughness elements. This work aims at analyzing these different terms, quantifying their respective contributions to the near-wall momentum budget, and providing guidance for their modeling. For this purpose, relevant data of turbulent flows are required. Roughness-resolved Reynolds-averaged Navier-Stokes simulations of transitionally and fully rough channel flows over academic roughness configurations are performed at high friction Reynolds numbers ranging from 3500 to 8000. Comparisons with existing and new velocity measurements performed in rough-wall turbulent boundary layers provide support to the simulation results, a particular emphasis being given on the validity of the numerical results in the wake of the roughness elements. These numerical results highlight the influence of roughness elements geometry and density on the roughness drag coefficient and the dispersive stress. It is particularly suggested that the standard roughness drag closure model should be revisited for double-averaged flows. Furthermore, the dispersive stress is shown to mainly originate from the wake of the roughness elements, an observation that could be leveraged for its modeling. However, since this stress contributes only marginally to the global stress and to the skin friction coefficient, such a modeling may not be critical at first order.