Estimating Dependence of the Turbulent Length Scales on Model Resolution Based on A Priori Analysis

Abstract

Abstract The Reynolds-averaged Navier–Stokes simulation (RANS) and the large-eddy simulation (LES) have been widely used to parameterize unresolved turbulent motions for the atmospheric boundary layer. However, there is an intermediate model resolution, termed terra incognita, in which neither RANS nor LES is appropriate. Although identifying an appropriate turbulent length scale is essential for an eddy-diffusivity model, it is still uncertain how transition of the length scale is between the LES and RANS regimes. In the present study, dependence of the turbulent length scale on the horizontal resolution of a numerical model is investigated using a priori analysis for a convective boundary layer to explore a turbulent parameterization scheme applicable to the terra incognita region. Here, the approaches for estimating the length scales derived from the dissipation rate of the turbulent kinetic energy and the eddy viscosity are proposed. The estimated length scale depends on both the horizontal and vertical grid sizes when the aspect ratio of the grid sizes is close to unity, while it tends to be insensitive to the vertical resolution and asymptotically converges to an upper limit as the aspect ratio increases. Analysis of the length scales divided into horizontal and vertical components reveals that anisotropy of the length scale is remarkable even though the aspect ratio is close to unity. This result suggests that the anisotropic effects of the turbulent flux in subgrid scales should be taken into consideration for a turbulence parameterization scheme.