Magnetic helicity flux in the presence of shear

Abstract

Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac &Cho. Magnetic helicity fluxes are explicitly gauge dependent however, and the correlations that have come to be called the Vishniac-Cho flux were determined in the Coulomb gauge, which turns out to be fraught with complications in shearing systems.While the fluxes of small-scale helicity are explicitly gauge dependent, their divergences can be gauge independent. We use this property to investigate magnetic helicity fluxes of the small-scale field through direct numerical simulations in a shearing-box system and find that in a numerically usable gauge the divergence of the small-scale helicity flux vanishes, while the divergence of the Vishniac-Cho flux remains finite.We attribute this seeming contradiction to the existence of horizontal fluxes of small-scale magnetic helicity with finite divergences. © 2011 The American Astronomical Society. All rights reserved.