Scale-dependent dynamic models for LES: Surface heterogeneity effects

An important challenge in large-eddy simulations of the atmospheric boundary layer over heterogeneous surfaces is the specification of the subgrid-scale (SGS) model coefficient(s) and, in particular, how to account for factors such as position in the flow, grid/filter scale and local atmospheric stability. Scale-dependent dynamic models have recently been developed to compute the Smagorinsky coefficient (Porté-Agel et al, J. Fluid Mech., 2000) and the SGS Schmidt/Prandtl number (Porté-Agel, Boundary-Layer Meteorol., 2004) at every time step and position in the flow based on the dynamics of the resolved scales. A series of simulations using these models with Lagrangian averaging (Meneveau et al, J. Fluid Mech., 1996) have been carried out of homogeneous and heterogeneous boundary layers (over patches of different sizes, aerodynamic roughness and surface heat flux). Simulations with the scale-dependent dynamic model yield the expected trends of the coefficients and scale-dependence parameters as function of position in the flow, local atmospheric stability and filter/grid scale. Furthermore, the new model gives improved predictions of mean profiles (similarity theory) and turbulence spectra as compared with the traditional scale-invariant dynamic model.