A52C-01 Addressing log-layer mismatch in wall modeled large eddy simulations over rough surfaces and canopies for geophysical flows (Invited)

Wall modeled large eddy simulations are a critical tool to perform scale-resolving simulations for boundary layer meteorology. To achieve computationally efficient predictions of very high Reynolds number planetary boundary layer flows, wall models are used to parameterize momentum, heat, and other exchanges at 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. Using 135 channel flow, 24 conventionally neutral boundary layer, and 12 truly neutral boundary layer wall modeled large eddy simulations, we elucidate how log-layer mismatch depends on the roughness length, displacement distance, matching velocity filtering strength, and vertical grid resolution. Using these simulations, we identify two sources of log-layer mismatch resulting from the wall model that appear even if the subgrid scale model and numerical grid are in principle well-designed. First, a spurious correlation between the friction velocity and the fluctuation of the matching velocity causes log-layer mismatch. This mechanism causes log-layer mismatch to grow as roughness length, displacement distance, and grid resolution increase. In other words, the log-layer mismatch error from the wall model can increase as the grid is refined. This error can be eliminated through spatial or temporal filtering of the matching velocity. However, the filter scale necessary to eliminate the error depends on the roughness parameters and grid resolution. Second, log-layer mismatch depends on the displacement distance that can be included in the wall model shear stress prediction over unresolved canopies. This additional source of error is not fixed by filtering the matching velocity. An analytical model of the log-layer mismatch stemming from the displacement distance is derived and validated against the large eddy simulations. The results demonstrate that the analytical model can predict the magnitude of this log layer mismatch based on a priori information about the simulation to within the uncertainty of the von Karman constant, enabling the use of the model to design large eddy simulations with minimum error from the wall model.