Scaling of high-order statistics in isotropic turbulence and how to measure them

Spatial distribution of various quantities in fluid turbulence is known to be highly-intermittent, especially for small-scales and high-order statistical measurements. Recently it was shown that intermittency emerges within velocity gradients, dissipation and enstrophy in incompessible flows at Taylor Reynolds number (R_λ) of order 10. High-order moments were shown to exhibit scaling at lower-R_λ than low-order moments did, meaning most extreme events exhibit turbulent behavior first. The scaling of velocity gradients at these R_λ has also been shown to be predictive of scaling of velocity differences with respect to scale size in the so-called inertial range (IR). This IR scaling is known to emerge within flows with R_λ  an order magnitude larger than those observed for velocity gradients. In this talk, we use highly resolved direct numerical simulations (DNS) to assess the emergence of scaling in IR for different order moments of velocity differences. The focus is to determine which orders exhibit scaling first and the width of scaling range at each order. We also develop sampling frequency criteria for estimating high-order moments of various quantities to discriminate between various theories that predict similar behavior at low-orders but differ significantly at high-orders.