Intermittency of Energy Dissipation in High-Resolution Direct Numerical Simulation of Turbulence

抄録

The statistics of energy dissipation rate \\ ildeε in turbulence and the ratio α_n≡ε_n+1⁄ε_n is studied using the data of direct numerical simulations of incompressible turbulence with up to 2048³ grid points, where ε_n is the average of \\ ildeε over a sphere of radius r_n with r_n⁄r_n+1=const>1. The data do not support the well-known assumption of the scale-independence of the statistics of α_n nor that of the statistical independence of α_n’s from each other, but suggest the existence of a scale range where the correlation between logα_n and logα_n+k is insensitive to n. A simple zero-cumulant approximation compatible with these observations yields an estimate of the moment ⟨(ε_n)^p⟩ for given ⟨logα_n⟩’s, in good agreement with the simulations for approximately |p|≤4.