Abstract
In recent years, Large-Eddy Simulation (LES) has been utilized as an useful tool to perform a numerical simulation for a planetary boundary layer. While parameterization schemes to represent the effect of subgrid scale motions have been proposed by many authors, properness of those schemes is still an open problem. In particular, parameterization of the subgrid scale is difficult in a stable boundary layer, in which the characteristic scale of turbulent eddies becomes smaller.
In this study, we perform a set of numerical simulations in a stable boundary layer with four types of subgrid scale parameterization schemes (Smagorinsky model, Dynamic Smagorinsky model, Deardorff model and Two-part model (Sullivan et al., 1994)). The obtained mean profile and second order flux are consistent with those of the intercomparison experiments by Beare et al. (2006). However, the vertical profile of the heat flux is different between the Smagorinsky and Deadorff types of parameterizations, even though the model resolution is fine.
Further, we examine self-consistency of those schemes in terms of the Germano identity in order to investigate the properness of the parameterized momentum and heat fluxes. Meneveau and Katz (1999) suggested that the Germano identity could gives explicitly the error at the scales between the grid and test filters and evaluated this error based on experimental data. We attempt to evaluate the error of the vertical flux with the data obtained from the numerical models. Our results suggest that the SGS heat flux tend to be underestimated with a coarser resolution in the Dynamic Smagorinsky model independently of the reference data, even though the model coefficient is determined so as to minimize the square error of the Germano identity. On the other hand, it is overestimated in the Deardorff and Two-part models.