Improving a Turbulence Scheme for the Terra Incognita in a Dry Convective Boundary Layer

Abstract

A new formulation for eddy viscosity and thermal eddy diffusivity is presented to constitute a turbulence closure model applicable to the terra incognita range. The Deardorff model, which is widely used for a Large-Eddy Simulation (LES), is extended to take into account the effect of anisotropic nature in the turbulent flux. The anisotropic length scales applied to the extended Deardorff model are empirically determined as a function of the model resolution using the results of the a priori LES analysis. The new model is examined with various horizontal resolutions for a convective boundary layer and is compared with the original Deardorff model. The new model improves the representation of the vertical heat flux and the magnitude of the resolved convection even for the resolutions including the terra incognita range. The original model tends to underestimate the subgrid heat flux with increasing the grid size; this underestimation causes artificial energy accumulation in higher wavenumbers. The proposed model suggests the feasibility of a turbulence scheme applicable to the terra incognita range, although the subgrid component tends to be overestimated in the LES range and the vertical temperature gradient in the surface layer is weakened for coarser model resolution.