Implicit Large Eddy Simulations of Boundary Layer Flows: Modeling Surface Roughness by Stochastic Microtopography

Large Eddy Simulations are widely used to study the Atmospheric Boundary Layer, since they resolve sufficient turbulence features to capture realistic boundary layer dynamics. For this purpose, the surface roughness of the terrain is often implemented by a roughness parameter that increases turbulence production near the surface through the stress tensor of the subgrid-scale model, in accordance with Monin-Obukhov theory. In Implicit Large Eddy Simulations, the absence of a subgrid-scale model simplifies implementation and reduces potential error sources at faster computational speeds, but does not permit the aforementioned implementation of the surface roughness. A drag coefficient can be used to integrate the effects of the surface roughness in Implicit Large Eddy Simulations. However, we propose a novel approach that models the surface roughness through a stochastic height variation of the lowest simulation layer. The method captures the impact of small-scale surface heterogeneity more effectively than a traditional uniform roughness parameter or drag coefficient model, while still just being controlled by a single parameter that prescribes the amplitude of the height variation. We find that this parameter has a linear correlation to the measured surface roughness in the corresponding simulation, with high numeric stability even for high wind speeds.