Wall Modelled LES of Heterogeneous Rough Surfaces*

Surface roughness is present in many applications in engineering and natural sciences. Its effect is not only that of increasing drag, but also of modifying the turbulence-generation cycle. Furthermore, heterogeneous roughness has an even more significant impact on the flow-field by inducing non-equilibrium effects. Resolved numerical simulations can provide useful insights on the flow state over rough walls, but are limited to low Reynolds-numbers. Wall-modelled large-eddy simulations (WMLES), on the other hand, allow us to reach high Reynolds numbers. In this work, WMLES were performed to simulate the flow over roughness strips placed normal to the mean flow. We compared the standard log-law based equilibrium wall-model with the generalized Moody-diagram model of Meneveau [J. Turbulence, 21(11):650–673, 2020] and with the Lagrangian Relaxation-Towards-Equilibrium (LaRTE) wall model [Fowler et al., J. Fluid Mech., 934(A44):1–37, 2022]. This model allows the inclusion of non-equilibrium effects in the response of the wall shear-stress to perturbations. A new formulation of the LaRTE model to rough walls is also proposed that allows the model to switch seamlessly between smooth-wall behaviour and transitionally or fully rough flow conditions. Applications of the extended LaRTE wall model are presented in the homogeneous rough-walls channel configuration and the in the normal-strips case.