Energy spectrum of tearing mode turbulence in sheared background field

TL;DR

This paper investigates the energy spectrum of tearing mode turbulence in sheared magnetic fields, revealing deviations from traditional turbulence spectra due to damping effects and scale-independent anisotropy, supported by numerical simulations.

Contribution

It introduces a theoretical model for tearing mode turbulence spectrum accounting for damping and anisotropy, validated by numerical simulations.

Findings

Energy spectrum deviates from a pure power law, showing exponential falloff.

Numerical simulations agree with the theoretical model.

Distinct turbulence features due to stable small-scale modes and scale-independent anisotropy.

Abstract

The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes stirs up a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction to the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects, one being the existence of many linearly stable small-scale modes which cause an effective damping during energy cascade; the other being the scale independent anisotropy induced by the large scale modes tilting the sheared background field, as opposed to the scale dependent anisotropy frequently encountered in traditional weak turbulence or critically balanced turbulence theory. These two differences result in the deviation of energy spectrum from a simple power law behavior, taking the form of a power law multiplied by an exponential falloff. Numerical simulation is carried out using viscous resistive MHD equations to verify our theoretical prediction, and reasonable agreement is found between numerical result and our model.