Cascades and dissipation ratio in rotating MHD turbulence at low magnetic Prandtl number

TL;DR

This paper develops a phenomenological model for isotropic MHD turbulence under rotation and magnetic fields, analyzing energy spectra and dissipation ratios at low magnetic Prandtl numbers using a shell model.

Contribution

It introduces a new phenomenology for rotating MHD turbulence with applied magnetic fields, including piecewise spectra and dissipation ratios for low magnetic Prandtl numbers.

Findings

Four types of spectra depending on key parameters.

Spectra and dissipation ratios computed for Pm ≤ 1.

Model predictions align with shell model simulations.

Abstract

A phenomenology of isotropic magnetohydrodynamic turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlations decay-time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and Alfv\'en wave period. For $Pm=1$ it leads to four kinds of piecewise spectra, depending on the four parameters, injection rate of energy, magnetic diffusivity, rotation rate and applied field. With a shell model of MHD turbulence (including rotation and applied magnetic field), spectra for $Pm \le 1$ are presented, together with the ratio between magnetic and viscous dissipation.