Role of helicity for large- and small-scale turbulent fluctuations

TL;DR

This paper investigates how helicity influences energy transfer and fluctuations in turbulent flows, revealing that even slight asymmetry in helical modes can reverse energy cascade direction and that intermittency depends on overall mode coupling.

Contribution

It introduces a parameter controlling helical mode asymmetry and provides the first numerical simulations from symmetric to fully helical turbulence, uncovering the impact on energy transfer and intermittency.

Findings

Energy cascade direction is singularly affected by helicity asymmetry.

Small-scale fluctuations and intermittency are highly sensitive to mode reduction.

Intermittency diminishes with even minor reduction in helical mode diversity.

Abstract

The effect of the helicity on the dynamics of the turbulent flows is investigated. The aim is to disentangle the role of helicity in fixing the direction, the intensity and the fluctuations of the energy transfer across the inertial range of scales. We introduce an external parameter, $\alpha$, that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present the first set of direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, $\alpha=0$, to the fully asymmetrical case, $\alpha=1$, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on $\alpha$, measuring a positive forward flux as soon as only a few modes with different helical polarities are present. On the other hand, small-scales fluctuations are sensitive only to the degree of mode-reduction, leading to a vanishing intermittency already for values of $\alpha \sim 0.1$ and independently of the degree of mirror symmetry-breaking. Our findings suggest that intermittency is the result of a global mode-coupling in Fourier space.