The Stretched-Vortex SGS Model in Physical Space

Abstract

The stretched-vortex subgrid stress model for the large-eddy simulation of turbulent flows has been developed to the stage where it can be applied to realistic flow at large Reynolds numbers [1] [2]. The basic assumption of this model [3] is that the subgrid vortex structure consists of straight, stretched vortices containing a nearly axisymmetric subgrid vorticity field. Vortices of this type, such as the Burgers vortex and the stretched-spiral vortex have provided fair quantitative estimates of turbulence fine-scale properties [4]. These structures are probably an oversimplified model of fine-scale turbulence, but may nevertheless contain sufficient of the vortex-stretching and energy cascade physics characteristic of the small scales to provide a reasonable basis for subgrid-stress modelling for LES. The resulting subgrid stresses are

$${{\tau }_{{ij}}} = K\left( {{{\delta }_{{ij}}} - e_{i}^{v}e_{j}^{v}} \right),$$

(1)

where K is the subgrid energy and e ^v _i , i = 1, 2, 3 are the direction cosines of the subgrid vortex axis. The local subgrid dissipation ϵ _sgs is equal to the product of K with the component of ${{\tilde{S}}_{{ij}}}$ aligned with the vortex axis. A class of simple models is obtained when it is assumed that the subgrid vortices are aligned with the eigenvectors of the rate-of-strain tensor ${{\tilde{S}}_{{ij}}}$ [1]. Utilizing an assumed Kolmogorov form for the local subgrid energy spectrum, the model estimates the turbulent energy production at the resolved-scale cutoff in terms of the model parameters ϵ and the Kolmogorov prefactor K ₀ and adjusts these parameters locally so as to continue the cascade through the cutoff to the subgrid vortex structures where the dissipation takes place.