Magnetic helicity and the evolution of decaying magnetohydrodynamic turbulence

TL;DR

This study uses ensemble high-resolution simulations to analyze magnetic helicity's role in the decay of magnetohydrodynamic turbulence, revealing persistent reverse spectral transfer even with decoupled momentum and induction equations.

Contribution

It demonstrates that reverse spectral transfer is a statistical property of MHD turbulence and introduces a new approach by decoupling the Lorentz force, enabling advanced analysis techniques.

Findings

Magnetic energy decay exponent determined as approximately 0.47 with Rλ dependence.

Reverse spectral transfer persists even when Lorentz force is removed.

New analysis methods enabled by linear induction equation with external velocity.

Abstract

Ensemble averaged high resolution direct numerical simulations of reverse spectral transfer are presented, extending on the many single realization numerical studies done up to now. This identifies this type of spectral transfer as a statistical property of magnetohydrodynamic turbulence and thus permits reliable numerical exploration of its dynamics. The magnetic energy decay exponent from these ensemble runs has been determined to be $n_E = (0.47 \pm 0.03) + (13.9 \pm 0.8)/R_{\lambda}$ for initially helical magnetic fields. We show for the first time that even after removing the Lorentz force term in the momentum equation, thus decoupling it from the induction equation, reverse spectral transfer still persists. The induction equation is now linear with an externally imposed velocity field, thus amenable to numerous analysis techniques. A new door has opened for analyzing reverse spectral transfer, with various ideas discussed.