Variational formulation of the Germano identity for the Navier–Stokes equations

The variational counterpart of the Germano identity for the large eddy simulation (LES) of turbulent flows is derived. The differences between the variational and the filter-based identities are explained on the basis of the role of an LES model in these two formulations. The variational Germano identity is then used to determine parameters in LES models. The performance of this identity in predicting the Smagorinsky eddy viscosity during the decay of homogeneous isotropic turbulence is evaluated. It is found that it yields results that are as accurate as its filter-based counterpart and that it is less sensitive to the exact approach used in evaluating the unknown parameters.

Acknowledgements

The support of ONR Grant No. 00014-02-1-0425 is gratefully acknowledged. The turbulent simulations were performed on the IBM p690 supercomputer made available through the Office of Information Technology [18] at Boston University.