Turbulent dynamo with advective magnetic helicity flux
  Many astrophysical bodies harbor magnetic fields that are thought to be
sustained by a dynamo process. However, it has been argued that the production
of large-scale magnetic fields by mean-field dynamo action is strongly
suppressed at large magnetic Reynolds numbers owing to the conservation of
magnetic helicity. This phenomenon is known as {\it catastrophic quenching}.
Advection of magnetic fields by stellar and galactic winds toward the outer
boundaries and away from the dynamo is expected to alleviate such quenching.
Here we explore the relative roles played by advective and turbulent--diffusive
fluxes of magnetic helicity in the dynamo. In particular, we study how the
dynamo is affected by advection. We do this by performing direct numerical
simulations of a turbulent dynamo of $\alpha^2$ type driven by forced
turbulence in a Cartesian domain in the presence of a flow away from the
equator where helicity changes sign. Our results indicate that in the presence
of advection, the dynamo, otherwise stationary, becomes oscillatory. We confirm
an earlier result for turbulent--diffusive magnetic helicity fluxes that for
small magnetic Reynolds numbers ($\Rm\lesssim 100...200$, based on the
wavenumber of the energy-carrying eddies) the magnetic helicity flux scales
less strongly with magnetic Reynolds number ($\Rm^{-1/2}$) than the term
describing magnetic helicity destruction by resistivity ($\Rm^{-1}$). Our new
results now suggest that for larger $\Rm$ the former becomes approximately
independent of $\Rm$, while the latter falls off more slowly. We show for the
first time that both for weak and stronger winds, the magnetic helicity flux
term becomes comparable to the resistive term for $\Rm\gtrsim 1000$, which is
necessary for alleviating catastrophic quenching.
