The structure of energy transfer in homogeneous turbulence

The filtering approach to scale decomposition in physical space leads to several energy evolution equations in incompressible flows. By comparing the statistics of the different inter-scale energy transfer terms that arise, we choose a novel optimal expression for the energy transfer which exhibits large-scale independence of the ratio of forward to backward energy flux, in addition to a milder filter-width dependence of this ratio than the classical subgrid-scale dissipation. We study the flow regions of intense energy transfer between resolved and subgrid scales from a geometrical point of view, to gain insight into the mechanism by which a predominant forward energy cascade is obtained in homogeneous 3D turbulence. The concept of length scale becomes a difficulty with this approach, because both a filter width $r$ and an object size $L$ are present. We show that with our energy transfer marker, $L$ depends on $r$ only to the extent that two regimes are observed: one above and one below $r\approx 30\eta$, where $\eta$ is the Kolmogorov length scale. Such a clear distinction is not observed with the usual expression for the subgrid-scale dissipation.