Energy transfers in shell models for MHD turbulence

TL;DR

This paper introduces a systematic method for deriving shell models in MHD turbulence that preserves key invariants and clarifies energy transfer mechanisms, enhancing understanding of energy fluxes in such systems.

Contribution

It presents a new systematic approach to derive shell models for MHD turbulence that maintains conservation laws and provides clear energy exchange definitions.

Findings

Reproduces known shell models with the new approach.

Suggests reinterpretation of energy fluxes in existing models.

Provides simple expressions for energy exchanges.

Abstract

A systematic procedure to derive shell models for MHD turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross-helicity and the magnetic helicity as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest neighbour shells, this procedure reproduces well known models but suggests a reinterpretation of the energy fluxes.