Statistics of energy transfer in the inertial subrange --Data analysis of high-resolution DNS of incompressible turbulence in a periodic box

Statistics of energy transfer in the physical and wave vector space are studied by using a series of high-resolution direct numerical simulations (DNS) of incompressible turbulence in a periodic box. The number of grid points in the DNS and the Taylor micro-scale Reynolds number $R_\lambda$ are up to $4096^3 $ and $1130$, respectively. We used two kinds of filtering ($S$) a spectral cutoff filter and ($G$) a Gaussian filter to define the grid scale (GS) and sub-grid scale (SGS) components. The DNS data suggest (i) the pdf's of energy transfer from GS to SGS components in ($G$) are more asymmetric in a systematic manner about the most probable value than those in ($S$), (ii) spectral eddy viscosity in ($G$) is almost constant ($\approx 0.35\big<\epsilon\big>^{1/3}k_c^{-4/3}$) for the wavenumber $k<0.8k_c$ provided that the cutoff wavenumber $k_c$ is in the inertial subrange, where $\big<\epsilon\big>$ is the mean rate of energy dissipation per unit mass, and (iii) the volume ratio of the backscatter region in ($G$) scales well with $k_c\eta$ irrespectively of $R_\lambda$ and is about $8\%$ in the inertial subrange, where $\eta$ is the Kolmogorov dissipation length.