Helically Decomposed Turbulence

TL;DR

This paper introduces a helical basis decomposition for analyzing energy and helicity fluxes in turbulent flows, revealing hidden inverse cascades and providing new insights into mode interactions.

Contribution

It proposes a novel formalism based on helical mode decomposition to analyze fluxes in turbulence, enabling separate investigation of helicity interactions.

Findings

Total energy flux splits into three constant fluxes in inertial range.

Presence of a negative flux indicating a hidden inverse cascade.

Helicity flux decomposes into two constant fluxes in inertial range.

Abstract

A decomposition of the energy and helicity fluxes in a turbulent hydrodynamic flow is proposed. The decomposition is based on the projection of the flow to a helical basis that allows to investigate separately the role of interactions among modes of different helicity. The proposed formalism is then applied in large scale numerical simulations of a non-helical and a helical flow, where the decomposed fluxes are explicitly calculated. It is shown that the total energy flux can be split in to three fluxes that independently remain constant in the inertial range. One of these fluxes that corresponds to the interactions of fields with the same helicity is negative implying the presence of an inverse cascade that is `hidden' inside the forward cascade. Similar to the energy flux the helicity flux is also shown that it can be decomposed to two fluxes that remain constant in the inertial range. Implications of these results as well possible new directions for investigations are discussed.