The Stretched-Vortex SGS Model in Physical Space

  • T. Voelkl
  • D. I. Pullin
  • R. D. Henderson
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 54)


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
$${{\tau }_{{ij}}} = K\left( {{{\delta }_{{ij}}} - e_{i}^{v}e_{j}^{v}} \right),$$
where K is the subgrid energy and e i v , 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.


Isotropic Turbulence Passive Scalar Spectral Element Method Large Reynolds Number Vortex Axis 
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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • T. Voelkl
    • 1
  • D. I. Pullin
    • 1
  • R. D. Henderson
    • 1
  1. 1.Graduate Aeronautical Laboratories 105-50California Institute of TechnologyPasadenaUSA

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