A Gradient Tensor–Based Subgrid-Scale Parameterization for Large-Eddy Simulations of Stratified Shear Layers Using the Weather Research and Forecasting Model

Abstract

The transition process from laminar stratified shear layer to fully developed turbulence is usually captured using direct numerical simulations, in which the computational cost is extremely high and the numerical domain size is limited. In this work, we introduce a scale-aware subgrid-scale (SGS) parameterization, based on the gradient tensor of resolved variables, which is implemented in the Weather Research and Forecasting (WRF) Model. With this new SGS model, we can skillfully resolve the characteristics of transition process, including formation of vortex cores, merging vorticity billows, breaking waves into smaller scales, and developing secondary instability in the stratified shear layer even at coarse-resolution simulations. Our new model is developed such that the time scales of the eddy viscosity and diffusivity terms are represented using the tensor of the gradient and not that of the rate-of-strain, which is commonly used in the parameterization of turbulent-viscosity models. We show that time scales of unresolved transition processes in our new model are correlated with those of vorticity fields. At early times, the power-law slopes in the kinetic and available potential energy spectra are consistent with the process of formation and merging waves with an upscale energy transfer. At later times, the power-law slopes are in line with the process of breaking waves into small-scale motions with a downscale transfer. More importantly, the efficiency of turbulent mixing is mainly high at the edge of vortex filaments and not at the vortices’ eyes. These findings can improve our understanding of turbulent mixing process in large-scale wind-induced events, such as tropical cyclones, using the WRF Model.