Addressing grid convergence and log-layer mismatch in wall modeled large eddy simulations over rough surfaces and canopies

Large eddy simulations of high Reynolds number boundary layer flows typically use wall models to represent the effects of the unresolved eddies near the surface on the resolved flow. However, wall modeled large eddy simulations (WMLES) can suffer from log-layer mismatch, characterized by a deviation of the predicted wall shear stress from its intended value. The dependence of the log-layer mismatch on parameters such as aerodynamic roughness length, displacement distance for canopies, grid resolution, and matching velocity choice is unclear. Here, we investigate these dependencies using a dataset of 171 WMLES cases, including channel flow and both conventionally and truly neutral boundary layers. We identify two sources of log-layer mismatch. The first stems from a spurious correlation between friction velocity and matching velocity fluctuation, intensified by increased roughness length, displacement distance, and finer grid resolution. This mismatch can be addressed by filtering the matching velocity, though the required strength of filtering depends on roughness parameters and grid resolution. The second source, arising from the inclusion of a displacement distance in the wall model, is not alleviated by filtering. We derive an analytical model based on a priori simulation parameters to predict log-layer mismatch magnitude within the uncertainty of the von Kármán constant. This model offers a practical guideline for designing WMLES over canopies.