Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

Mahendra Verma,Shadab Alam,Manohar Sharma,Soumyadeep Chatterjee

doi:10.3390/fluids6060225

Mahendra Verma, Shadab Alam + Show 2 more

Open Access

https://doi.org/10.3390/fluids6060225

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Abstract

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

Highlights

Magnetohydrodynamics (MHD) provides a framework to study the dynamics of flows in interstellar medium, galaxies, accretion disks, stars and planet interiors, solar wind, Tokamak, etc. [1]
Dar et al [5] and Verma [6] showed that MHD turbulence has six energy fluxes related to the velocity and magnetic fields
The energy fluxes of MHD turbulence provide a measure for these transfers

Summary

Introduction

Magnetohydrodynamics (MHD) provides a framework to study the dynamics of flows in interstellar medium, galaxies, accretion disks, stars and planet interiors, solar wind, Tokamak, etc. [1]. Dar et al [5] and Verma [6] showed that MHD turbulence has six energy fluxes related to the velocity and magnetic fields. Verma et al [7] showed that in a typical turbulent magnetofluid, the inertial-range kinetic energy flux is depleted due to the energy transfer from the velocity to the magnetic field. Marsch [13] argued that in the absence of a mean magnetic field, the energy spectra of Elsässer variables exhibit a k−5/3 spectra. Verma et al [28] estimated the energy flux in the solar wind using the energy spectrum and assuming Kolmogorov-like turbulence phenomenology for the MHD turbulence [13]. We compute the various energy fluxes of forced MHD turbulence and validate several exact relations with numerical results.

Energy Fluxes and Exact Relations

Governing Equations and Simulation Method

Numerical Results on the Energy Fluxes

Conclusions