New Exact Betchov-like Relation for the Helicity Flux in Homogeneous Turbulence

TL;DR

This paper extends the formalism of energy flux decomposition in turbulence to include kinetic helicity transfer, deriving a new exact relation that quantifies the physical mechanisms contributing to helicity flux across scales.

Contribution

It introduces a novel exact relation for helicity flux in turbulence, revealing the dominant physical processes and their quantitative contributions, analogous to the Betchov relation for energy.

Findings

Vortex flattening and twisting account for about 50% of helicity flux.

The mean contribution of vortex flattening is three times larger than twisting.

Multi-scale effects contribute the remaining flux with approximate equipartition.

Abstract

In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3(2021)). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. About 50% of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50% of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling.