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 _λ 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 α (kL)^αS , F α (kL)^αF in the inertial subrange, where α_S ∼ 2/3, α_F ∼ 1 and L the characteristic length scale of energy containing eddies. The comparison between the statistics of T, the energy dissipation rate ε and its average ε_r over a domain of scale r shows that T is less intermittent than ε, while there is a certain similarity between the probability distribution functions of T and ε_r.