Title: Large-scale dynamos in rapidly rotating plane layer convection,
Abstract: Context: Convectively-driven flows play a crucial role in the dynamo
processes that are responsible for producing magnetic activity in stars and
planets. It is still not fully understood why many astrophysical magnetic
fields have a significant large-scale component. Aims: Our aim is to
investigate the dynamo properties of compressible convection in a rapidly
rotating Cartesian domain, focusing upon a parameter regime in which the
underlying hydrodynamic flow is known to be unstable to a large-scale vortex
instability. Methods: The governing equations of three-dimensional nonlinear
magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes
are compared and we propose a possible benchmark case for other similar codes.
Results: In keeping with previous related studies, we find that convection in
this parameter regime can drive a large-scale dynamo. The components of the
mean horizontal magnetic field oscillate, leading to a continuous overall
rotation of the mean field. Whilst the large-scale vortex instability dominates
the early evolution of the system, it is suppressed by the magnetic field and
makes a negligible contribution to the mean electromotive force that is
responsible for driving the large-scale dynamo. The cycle period of the dynamo
is comparable to the ohmic decay time, with longer cycles for dynamos in
convective systems that are closer to onset. In these particular simulations,
large-scale dynamo action is found only when vertical magnetic field boundary
conditions are adopted at the upper and lower boundaries. Strongly modulated
large-scale dynamos are found at higher Rayleigh numbers, with periods of
reduced activity ("grand minima"-like events) occurring during transient phases
in which the large-scale vortex temporarily re-establishes itself, before being
suppressed again by the magnetic field.