Statistics of Energy Transfer in High-Resolution Direct Numerical Simulation of Turbulence in a Periodic Box

Abstract

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 ∝( k L ) α S , F ∝( k L ) α F 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 .