Signatures of non-universal large scales in conditional structure functions from various turbulent flows

Abstract

We present a systematic comparison of conditional structure functions in nine turbulent flows. The flows studied include forced isotropic turbulence simulated on a periodic domain, passive grid wind tunnel turbulence in air and in pressurized SF6, active grid wind tunnel turbulence (in both synchronous and random driving modes), the flow between counter-rotating discs, oscillating grid turbulence and the flow in the Lagrangian exploration module (in both constant and random driving modes). We compare longitudinal Eulerian second-order structure functions conditioned on the instantaneous large-scale velocity in each flow to assess the ways in which the large scales affect the small scales in a variety of turbulent flows. Structure functions are shown to have larger values when the large-scale velocity significantly deviates from the mean in most flows, suggesting that dependence on the large scales is typical in many turbulent flows. The effects of the large-scale velocity on the structure functions can be quite strong, with the structure function varying by up to a factor of 2 when the large-scale velocity deviates from the mean by ±2 standard deviations. In several flows, the effects of the large-scale velocity are similar at all the length scales we measured, indicating that the large-scale effects are scale independent. In a few flows, the effects of the large-scale velocity are larger on the smallest length scales.