A vortex-based subgrid stress model for large-eddy simulation

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Abstract
A class of subgrid stress (SGS) models for large-eddy simulation (LES) is presented based on the idea of structure-based Reynolds-stress closure. The subgrid structure of the turbulence is assumed to consist of stretched vortices whose orientations are determined by the resolved velocity field. An equation which relates the subgrid stress to the structure orientation and the subgrid kinetic energy, together with an assumed Kolmogorov energy spectrum for the subgrid vortices, gives a closed coupling of the SGS model dynamics to the filtered Navier–Stokes equations for the resolved flow quantities. The subgrid energy is calculated directly by use of a local balance between the total dissipation and the sum of the resolved-scale dissipation and production by the resolved scales. Simple one- and two-vortex models are proposed and tested in which the subgrid vortex orientations are either fixed by the local resolved velocity gradients, or rotate in response to the evolution of the gradient field. These models are not of the eddy viscosity type. LES calculations with the present models are described for 323 decaying turbulence and also for forced 323 box turbulence at Taylor Reynolds numbers Rλ in the range Rλ≃30 (fully resolved) to Rλ=∞. The models give good agreement with experiment for decaying turbulence and produce negligible SGS dissipation for forced turbulence in the limit of fully resolved flow.

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