A tensor invariant approach to energy flux in magnetohydrodynamic turbulence

TL;DR

This paper introduces a tensor invariant-based framework to analyze energy flux mechanisms in magnetohydrodynamic turbulence, linking field configurations to energy transfer processes.

Contribution

It formalizes the use of tensor invariants as proxies for energy flux mechanisms and expresses hydrodynamic flux contributions exactly in terms of velocity gradient invariants.

Findings

Tensor invariants act as proxies for energy flux under specific conditions.

Invariants bound the energy flux for different physical mechanisms.

Results demonstrated with 3D MHD turbulence simulations.

Abstract

A scale-by-scale analysis of energy flux in the turbulent cascade can be performed using the spatially filtered magnetohydrodynamic (MHD) equations, while the gradient tensor invariants are widely used to characterise the structure of velocity and magnetic fields. Physical mechanisms responsible for energy flux require specific field configurations whose strength is quantified by these tensor invariants. We explore this requirement, showing that the tensor invariants act as proxies for mechanistic energy fluxes under quantifiable conditions. As a special case, the purely hydrodynamic contributions to energy flux can be expressed exactly in terms of the invariants of the velocity gradient tensor. We also show that the invariants bound the available energy flux for distinct physical mechanisms, formalising the idea that each transfer mechanism requires field configurations with gradients of sufficient strength to support a given energy flux. Results are illustrated using 3D simulations of freely decaying MHD turbulence.