Statistics of energy transfer in high-resolution direct numerical simulation of turbulence in a periodic box

The statistics of energy transfer is studied by using the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence in a periodic box with the Taylor micro-scale Reynolds number R-lambda and grid points up to approximately 1130 and 4096(3), respectively. The data show that the energy transfer T across the wave number k is highly intermittent and the skewness S and flatness F of T increase with k approximately as S proportional to (kL)(alpha S), F proportional to (kL)(alpha F) in the inertial subrange, where alpha(S) similar to 2/3, alpha(F) similar to 1 and L the characteristic length scale of energy containing eddies. The comparison between the statistics of T, the energy dissipation rate epsilon and its average epsilon(r) over a domain of scale r shows that T is less intermittent than epsilon, while there is a certain similarity between the probability distribution functions of T and epsilon(r).