Helicity statistics in homogeneous and isotropic turbulence and turbulence models

TL;DR

This paper investigates the statistical properties and scaling behaviors of helicity in homogeneous isotropic turbulence and related shell models, revealing mirror symmetry recovery at small scales and analyzing high-order structure functions.

Contribution

It introduces new correlation functions based on vorticity and velocity increments that are sensitive to mirror symmetry breaking and studies their scaling in turbulence and shell models.

Findings

Mirror symmetry is recovered at small scales.

Chiral terms are subleading and follow dimensional plus anomalous corrections.

High Reynolds number shell models support the findings.

Abstract

We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small-scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.