A dynamic model for large-eddy simulation of boundary layer flow over rough, multiscale surfaces

The Monin-Obukhov (MO) similarity theory is a widely-used approach for specification of wallstress boundary conditions in large-eddy simulation (LES) of flow over homogeneously-distributed roughness. In using MO, an empirical hydrodynamic roughness length represents drag effects from roughness modes finer than the filter width, D, in a LES. The spatial height distribution of many natural surfaces is multiscale, and can be described with a power law exponent; additionally, and like atmospheric boundary layer (ABL) turbulence, these surfaces can be composed of spatial length scales ranging from the meteorological mesoscale to diffusive length scales far smaller than D. LES of ABL flow over a multiscale surface requires significant generalization of the standard wallstress boundary conditions. Here, we propose that such a generalization is achieved by spatially filtering the surface at D, thereby separating the surface into resolved and subgrid-scale (SGS) components. The resolved component is represented with the surface-gradient based drag (SGD) model, a recently developed pressure drag model applicable to the unique case considered here in which surface undulations are horizontally resolved but vertically unresolved (Anderson and Meneveau, 2010: Boundary-Layer Meteorol., submitted). The SGS component is modeled with modified MO theory, in which the hydrodynamic roughness length becomes an effective hydrodynamic roughness length that is proportional to the product of root-mean-square of the SGS height and a dimensionless model parameter, the SGS roughness index. The index is unknown and must be numerically evaluated. A dynamic approach is presented, wherein the index is evaluated through application of the Germano identity to the plane-averaged ground-level total wallstress (MO+SGD) at two filter widths (grid- and test-filter widths, Germano et al., 1991: Phys. Fluids A, 3, 1760—1765), and assuming scale-invariance. We call this approach the dynamic surface roughness (DSR) model, and test it in a suite of LESs of ABL flow over synthetic, fractal-like landscapes. Effects of spatial resolution and spectral slopes (changing from ``rough'' to ``smooth'') are investigated. In all cases the model is numerically stable. For the majority of surfaces considered the DSR model predicts resolution-invariant results.