Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain

The accuracy of large-eddy simulations (LESs) of the atmospheric boundary layer (ABL) over complex terrain relies on the ability of the subgrid-scale (SGS) models to capture the effect of subgrid turbulent fluxes on the resolved fields of velocity and scalars (e.g., heat, water vapor, and pollutants). A common approach consists of parameterizing the SGS stresses and fluxes using eddy viscosity and eddy diffusivity models, respectively. These models require the specification of two parameters: the Smagorinsky coefficient in the eddy viscosity model and, in addition, the SGS Schmidt/Prandtl number in the eddy diffusivity model. This is complicated by the dependence of the coefficients on local conditions such as distance to the ground, mean shear, and atmospheric stability. In this study, scale-dependent dynamic SGS models are used in conjunction with Lagrangian averaging to compute both the Smagorinsky coefficient and the SGS Schmidt (or Prandtl) number dynamically as the flow evolves in both space and time based on the local dynamics of the resolved scales. These tuning-free models are implemented in LES of both homogeneous and heterogeneous neutral atmospheric boundary layers with surface fluxes of a passive scalar. In the homogeneous simulations the models are shown to accurately predict the resolved flow statistics (mean profiles and spectra of velocity and scalar concentration) and spatial distributions of the SGS model coefficients and parameters. In simulations over heterogeneous surfaces both coefficients adjust in a self-consistent way to horizontal flow inhomogeneities associated with changes in surface conditions. For smooth-to-rough (rough-to-smooth) abrupt changes in surface roughness the Smagorinsky coefficient decreases (increases) in response to increased (decreased) mean shear and flow anisotropy associated with these transitions. The SGS Schmidt number also adjusts to inhomogeneities in the scalar field associated with changes in surface scalar flux. This illustrates the need for local calculation of model coefficients and brings into question the common practice of using a constant SGS Schmidt/Prandtl number in LES of the ABL.