Magnetic helicity transport in the advective gauge family

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal takes the form of a purely advective flux. Numerical simulations of turbulence in this advective gauge family exhibit instabilities triggered by build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, vector potential is evolved in a numerically well behaved gauge, from which the advective potential is obtained by a gauge transformation. In the kinematic regime, the magnetic density evolves similarly to a passive scalar when resistivity is small and turbulent mixing mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive to the magnetic helicity flux in the advective gauge are found to be significant owing the development of small length scales in the irrotational part of the magnetic vector potential.