A Large-Eddy Simulation Model for Boundary-Layer Flow Over Surfaces with Horizontally Resolved but Vertically Unresolved Roughness Elements

Accurate prescription of ground-level boundary conditions is a key requirement for large-eddy simulation (LES) of atmospheric boundary-layer (ABL) flow. When the lower boundary is a homogeneously rough surface, the Monin-Obokhov (MO) similarity theory is a well-tested approach for specification of the boundary fluxes. This approach requires an empirically calibrated hydrodynamic roughness length to represent the aggregate effects of all flow-resisting surface details at unresolved scales, and a displacement height to represent a vertical shift in the velocity profiles. For cases in which the surface height distribution varies slowly enough in the horizontal direction that it is spatially resolvable in the LES, but where the height itself is small enough to fall below the first vertical grid point, special challenges arise. First, it is shown herein that prescription of a horizontally varying displacement height, in the context of MO similarity, is insufficient to produce realistic results in this unique application. A subsequent approach, which is relatively easy to implement, and can be used in LES without the need to use a "terrain-following" coordinate system or computationally expensive alternatives such as local grid refinement, is proposed. The approach is based on a form drag expressed in terms of the frontal area and the corresponding incoming momentum flux of the flow. The frontal area is evaluated in terms of the flow-normal gradient of the resolved height distribution. The proposed model, named the surface gradient-based drag (SGD) model, is applied to a variety of rough surfaces for which appropriate data exist. These surfaces are horizontally resolved, but vertically unresolved. The resulting mean velocity distributions are compared with available data and good agreement is observed. In addition, we apply the SGD model in flow over two synthetic multiscale surfaces with prescribed, power-law surface-height spectra. For these cases, first- and second-order flow statistics agree with established results. Future perspectives are outlined.