Asymmetry of velocity increments in turbulence

TL;DR

This paper investigates the asymmetry of velocity increments in high-Reynolds-number turbulence using direct numerical simulations, revealing that high-order structure functions are dominated by negative velocity increments and offering new dynamical insights.

Contribution

It uncovers the fundamental asymmetry in velocity increments neglected by existing models and explains the dominance of negative increments in high-order structure functions.

Findings

High-order structure functions mainly originate from negative velocity increments.

Asymmetry affects the non-monotonic behavior of structure function moments.

Differences between ordinary and absolute structure functions are explained by this asymmetry.

Abstract

We use well-resolved direct numerical simulations of high-Reynolds-number turbulence to study a fundamental statistical property of turbulence -- the asymmetry of velocity increments -- with likely implications on important dynamics. This property, ignored by existing small-scale phenomenological models, manifests most prominently in the non-monotonic trend of velocity increment moments (or structure functions) with the moment order, and in differences between ordinary and absolute structure functions for a given separation distance. We show that high-order structure functions arise nearly entirely from the negative side of the probability density of velocity increments, essentially removing the ambiguity between ordinary and absolute moments, and provide a plausible dynamical interpretation of this result.