Statistics of Intense Turbulent Vorticity Events

TL;DR

This paper derives an analytical probability distribution function for vorticity fluctuations in fully developed turbulence, revealing the statistical nature of intense vorticity events through a novel phase-space and instanton-based approach.

Contribution

It introduces a new analytical method combining phase-space restriction and instanton calculus to describe vorticity statistics in turbulence.

Findings

Derived a closed-form vorticity PDF at high Reynolds numbers

Revealed the intermittent nature of vorticity fluctuations

Provided a theoretical framework for turbulence vorticity statistics

Abstract

We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term correlated at large scales, we obtain in the high Reynolds number regime a closed analytical expression for the probability distribution function of an arbitrary component of the vorticity field. The central idea underlying the analysis consists in the phase-space restriction to a particular sector where the rate of strain and the rotation tensors can be locally regarded as slow and fast degrees of freedom, respectively. This prescription is implemented along the Martin-Siggia-Rose functional framework, whereby instantons and perturbations around them are taken into account within a steepest-descent approach.