Anisotropic Models of Energy Transfer to the Subgrid for LES of Anisotropic Turbulence

Most currently available LES subgrid models assume unresolved turbulence to be isotropic. They therefore represent the transfer of energy to subgrid scales as isotropic. However, in LES of complex turbulent flows, where LES resolution is necessarily coarse, this assumption is generally invalid. In this case, the anisotropy of the unresolved turbulence needs to be accounted for, and in particular, accurately representing the anisotropy of the energy transfer to the subgrid is a necessary condition for predicting the resolved Reynolds stress. Furthermore, the subgrid turbulence also makes a significant contribution to the Reynolds stress. A tensor eddy viscosity subgrid model is proposed that is formulated in terms of the second moment of the resolved velocity gradient tensor. This is a fourth-rank tensor that encodes the anisotropy of the subgrid turbulence and thus allows the effects of anisotropy to be represented. The model's performance is assessed using a statistical a priori analysis based on filtered DNS simulations of a wide variety of homogeneous anisotropic test cases created by anisotropically forcing homogeneous turbulence. These DNS data will also be compared to the results of preliminary LES using the proposed model to determine the a posteriori performance of the model.