Addressing Grid Convergence and Log-Layer Mismatch in Wall Modeled Large Eddy Simulations of Geophysical Flows Over Rough Surfaces and Canopies

Wall modeled large eddy simulations are the primary scale-resolving method used to investigate boundary layer meteorology. Wall models are used to parameterize momentum, heat, and other exchanges at the surface to achieve computationally efficient predictions given the very high Reynolds numbers of planetary boundary layers and the importance of small-scales near the surface. However, wall modeled large eddy simulations can be contaminated by log-layer mismatch, where the prediction of wall shear stress (friction velocity) deviates from the intended value. It is not clear how this log-layer mismatch in boundary layers depends on parameters that represent unresolved roughness elements and on the computational setup. This study elucidates how log-layer mismatch depends on the roughness length, displacement distance, matching velocity filtering strength, and vertical grid resolution using 135 channel flow, 24 conventionally neutral boundary layer, and 12 truly neutral boundary layer wall modeled large eddy simulations. The results demonstrate two sources of log-layer mismatch. First, a spurious correlation between the friction velocity and the fluctuation of the matching velocity causes log-layer mismatch that increases with roughness length, displacement distance, and increasing grid resolution. This log-layer mismatch can be eliminated by filtering the matching velocity, but the filter timescale necessary to eliminate the error depends on the roughness parameters and grid resolution. Second, an additional source of log-layer mismatch is identified, depending on the displacement distance. This mechanism of log-layer mismatch is not alleviated by filtering the matching velocity. An analytical model of this log-layer mismatch mechanism is derived and validated against the large eddy simulations. The results demonstrate that the analytical model is able to predict the magnitude of this log layer mismatch based on a priori information about the simulation to within the uncertainty of the von Kármán constant.