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 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 / ðkLÞ S , F / ðkLÞ F in the inertial subrange, where S $ 2=3, F $ 1 and L the characteristic length scale of energy containing eddies. The comparison between the statistics of T, the energy dissipation rate and its average r over a domain of scale r shows that T is less intermittent than , while there is a certain similarity between the probability distribution functions of T and r .

Energy Transfer from Large to Small Scales in Turbulence by Multiscale Nonlinear Strain and Vorticity Interactions

“…In this way, the steep slope of the curves in Figure 7 underscore that the nonlocal terms in (12) are mostly determined by scales only slightly smaller than . This result demonstrates the concept of the 'leaky cascade' [9,14,33,[53][54][55][56][57] in terms of multi-scale vorticity-strain interactions.…”

The anisotropic structure of turbulence and its energy spectrum

“…That is, anisotropy of the small-scales is observed, 15,16 and direct scale interactions across the whole scale range exist with significant energy transfer to the small as well as the large scales. [17][18][19] A revised conceptual picture of the turbulent motions in physical space is thus needed, which, moreover, is consistent with the observed spectral scaling.…”

Interfaces and inhomogeneous turbulence

“…Computations of the energy transfer T (x, k) between different length scales show [42] that upscale transfer (from small to large) is almost as large (within 10%) as the downscale transfer, which has generally been assumed to be dominant and the most important process governing the small-scale structure of turbulence [43,44]. New results show that T (x, k) is very intermittent; its fluctuations being much larger than its mean value.…”