Finite Dissipation in Anisotropic Magnetohydrodynamic Turbulence

TL;DR

This study investigates how an external magnetic field influences energy dissipation in anisotropic magnetohydrodynamic turbulence, revealing that dissipation rates stabilize at finite values as Reynolds number increases, with implications for space and astrophysical turbulence modeling.

Contribution

The paper provides the first numerical confirmation that dissipation rates in anisotropic MHD turbulence asymptote to finite values at high Reynolds numbers under varying magnetic field strengths.

Findings

Dissipation rate approaches a finite value as Reynolds number increases.

Mean magnetic field suppresses initial dissipation but stabilizes at a constant for strong fields.

RMHD results align closely with high mean-field 3D MHD simulations.

Abstract

In presence of an externally supported, mean magnetic field a turbulent, conducting medium, such as plasma, becomes anisotropic. This mean magnetic field, which is separate from the fluctuating, turbulent part of the magnetic field, has considerable effects on the dynamics of the system. In this paper, we examine the dissipation rates for decaying incompressible magnetohydrodynamic (MHD) turbulence with increasing Reynolds number, and in the presence of a mean magnetic field of varying strength. Proceeding numerically, we find that as the Reynolds number increases, the dissipation rate asymptotes to a finite value for each magnetic field strength, confirming the K\'arm\'an-Howarth hypothesis as applied to MHD. The asymptotic value of the dimensionless dissipation rate is initially suppressed from the zero-mean-field value by the mean magnetic field but then approaches a constant value for higher values of the mean field strength. Additionally, for comparison, we perform a set of two-dimensional (2DMHD) and a set of reduced MHD (RMHD) simulations. We find that the RMHD results lie very close to the values corresponding to the high mean-field limit of the three-dimensional runs while the 2DMHD results admit distinct values far from both the zero mean field cases and the high mean field limit of the three-dimensional cases. These findings provide firm underpinnings for numerous applications in space and astrophysics wherein von K\'arm\'an decay of turbulence is assumed.