Asymmetry of velocity increments in turbulence

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 nonmonotonic 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.