Large-Eddy Simulation of Stratified Turbulence. Part I: A Vortex-Based Subgrid-Scale Model

Abstract

Abstract The stretched-vortex subgrid-scale (SGS) model is extended to enable large-eddy simulation of buoyancy-stratified turbulence. Both stable and unstable stratifications are considered. The extended model retains the anisotropic form of the original stretched-vortex model, but the SGS kinetic energy and the characteristic SGS eddy size are modified by buoyancy subject to two constraints: first, the SGS kinetic energy dynamics is determined by stationary and homogeneous conditions, and second, the SGS eddy size obeys a scaling analogous to the Monin–Obukhov similarity theory. The SGS model construction, comprising an ensemble of subgrid stretched-vortical structures, naturally limits vertical mixing but allows horizontal mixing provided the alignment of the SGS vortex ensemble is favorable, even at high nominal gradient Richardson numbers. In very stable stratification, the model recovers the z-less limit, in which a vortex-based Obukhov length controls the SGS dynamics, while in very unstable stratification, the model recovers the free-convection limit, in which a vortex-based Deardorff velocity controls the SGS dynamics. The efficacy of the present SGS model is demonstrated by simulating the canonical stationary and homogeneous, stratified sheared turbulence at high Reynolds numbers and moderately high Richardson numbers. In the postprocessing, the SGS dynamics of the stretched-vortex model is further interrogated to yield predictions of buoyancy-adjusted one-dimensional SGS spectra and SGS root-mean-square velocity-derivative fluctuations.