The equation for the kinetic energy based on the residual (sub-filter) velocity is written in several ways in which each term in the equation is Galilean invariant. A different expression for the inter-scale energy transfer term arises from each equation. The statistics of these different terms are studied, together with those of the subgrid-scale (SGS) dissipation. We report on the expression yielding the variance which best matches that of the SGS dissipation, and which is most negatively correlated with it. We argue why the term exhibiting these features is preferred over the others based on its physical meaning. Our study used direct numerical simulation data of homogeneous isotropic turbulence, and our conclusions were observed to be valid with both Gaussian and sharp spectral (low-pass) filters.
The equation for the kinetic energy based on the residual (sub-filter) velocity is written in several ways in which each term in the equation is Galilean invariant. A different expression for the inter-scale energy transfer term arises from each equation. The statistics of these different terms are studied, together with those of the subgrid-scale (SGS) dissipation. We report on the expression yielding the variance which best matches that of the SGS dissipation, and which is most negatively correlated with it. We argue why the term exhibiting these features is preferred over the others based on its physical meaning. Our study used direct numerical simulation data of homogeneous isotropic turbulence, and our conclusions were observed to be valid with both Gaussian and sharp spectral (low-pass) filters. Read More
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