Assessment of a coupled momentum and passive scalar flux subgrid-scale turbulence model for large-eddy simulation of flow in the planetary boundary layer

We previously developed a linear algebraic subgrid-scale stress (LASS) model, which includes production, dissipation, and pressure redistribution terms. Results of large-eddy simulations at various resolutions of a neutrally-stratified boundary layer flow over a flat, rough surface indicate that the LASS model is a more physically complete subgrid-scale (SGS) stress turbulence model that provides near-wall anisotropies that eddy-viscosity models do not, and yields proper shear stress values in the logarithmic layer. We have also examined the combination of the LASS model with reconstruction, using the approximate deconvolution model, of the subfilter-scale stress (Chow et al., J Atmos Sci 62, 2005, 2058ff). With our mixed model we are able to represent both anisotropy and energy backscatter at both the subfilter- and subgrid- scales.

In this paper, we extend our previous work to be applicable to a range of atmospheric stability conditions for the dry atmosphere by adding a passive algebraic subgrid-scale heat flux model, which includes scalar production and pressure redistribution terms. The SGS stresses are solved as a system of linear equations and are then coupled to the set of equations that model the SGS heat flux. We refer to the set of SGS stress-heat flux equations as the generalized linear algebraic subgrid-scale (GLASS) model. In addition to near-wall stress anisotropy, GLASS represents the SGS heat flux anisotropy for wall-bounded flows that isotropic eddy diffusion models cannot. The heat transport in the temperature field of wall-bounded shear flows is known to be anisotropic at inertial and dissipative scales (Warhaft, Annu Rev Fluid Mech 32, 2000, 203ff).

We apply GLASS to large-eddy simulations of idealized atmospheric convective and stable boundary layers. Our sheared convective boundary layer LES mimics the constant geostrophic forcing case of Fedorovich et al. (16th BLT, 2004, Paper P4.7). For model comparison, we create a moderate stable boundary layer as in Zhou and Chow (J Atmos Sci 68, 2011, 2142ff). For both boundary layer cases, GLASS predicts the evolution of resolved and SGS turbulent quantities at least as well as the LESs with diffusion models, while including additional physics. Notably, results of these simulations and previous resolution studies show that GLASS overcomes the need to alter model coefficients for different positions in the flow, grid/filter aspect ratios, and atmospheric stabilities, etc.