Scale resolved intermittency in turbulence

Abstract

The deviations $δζ_m$ ("intermittency corrections") from classical ("K41") scaling $ζ_m=m/3$ of the $m^{th}$ moments of the velocity differences in high Reynolds number turbulence are calculated, extending a method to approximately solve the Navier-Stokes equation described earlier. We suggest to introduce the notion of scale resolved intermittency corrections $δζ_m(p)$, because we find that these $δζ_m(p)$ are large in the viscous subrange, moderate in the nonuniversal stirring subrange but, surprisingly, extremely small if not zero in the inertial subrange. If ISR intermittency corrections persisted in experiment up to the large Reynolds number limit, our calculation would show, that this could be due to the opening of phase space for larger wave vectors. In the higher order velocity moment $\langle|u(p)|^m\rangle$ the crossover between inertial and viscous subrange is $(10ηm/2)^{-1}$, thus the inertial subrange is {\it smaller} for higher moments.