Optimizing subgrid-scale closure constants for spectral energy transfer in homogeneous turbulence

The inter-scale energy flux of turbulent flows is used to optimize subgrid-scale (SGS) models. Using a wavelet multiresolution framework, the spectral energy flux due to the triadic interactions is estimated given a nominal grid cutoff scale of large-eddy simulation (LES). For a prescribed algebraic SGS closure, its constant is optimized a priori so that the modeled SGS dissipation balances the inter-scale energy transfer. The formulation is tested for incompressible homogeneous isotropic turbulence. For one-parameter eddy-viscosity models, the Smagorinsky constant is obtained if a cutoff scale is in the inertial subrange, consistent to the theoretical prediction. A posteriori results show that the dynamic estimation of the Smagorinsky model constant is consistent to a priori optimization and the dynamic model is spectrally optimal if the LES grid resolves the inertial subrange. The optimization is also performed for a two-parameter Clark-type model and a four-parameter tensor-coefficient-based Smagorinsky model, describing the roles of the individual closure terms.