Robustness of oscillatoryα²dynamos in spherical wedges

Abstract

Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells. Aims. We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos. Methods. We solve the equations for one-dimensional time-dependent α 2 and α 2 Ω mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle θ 0 between the latitudinal boundaries and the poles in spherical coordinates.Results. In the case of constant α and η t profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and α profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on θ 0 . When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions. A reduced α effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and reproduces best the solutions in spherical wedges. For weak shear, oscillatory solutions are obtained only for perfect conductor field conditions and negative shear. Oscillatory solutions become preferred at sufficiently strong shear. Recent three-dimensional dynamo simulations producing solar-like magnetic activity are expected to lie in this range.

Influence of a coronal envelope as a free boundary to global convective dynamo simulations

“…We find that the dynamo properties are generally strongly influenced by the choice of boundary conditions. This can be particularly important when the magnetic field is strong near the boundary, as was seen recently in connection with the latitudinal boundary condition for simple α 2 mean-field dynamos (Cole et al 2016) in the wedge geometry that we consider here too. In all of our simulations a toroidal field tends to form preferentially near the surface of the convection zone but it is pushed down by a radial field boundary condition.…”

Advances in mean-field dynamo theory and applications to astrophysical turbulence

“…Masada & Sano (2014) confirmed this finding for a dynamo in Cartesian geometry and reinforced the suggestion that the solar dynamo might indeed be of α 2 type. Then, Cole et al (2016) found that the oscillatory α 2 dynamo requires highly conducting plasma at high latitudes or, alternatively, a perfectly conducting boundary condition at high latitudes, as is often assumed in spherical wedge simulations (Mitra et al 2009). This was then confirmed through the realization that an oscillatory migratory α 2 dynamo is possible even with constant α effect provided there are two different boundary conditions on the two sides (Brandenburg 2017).…”

Convection-driven spherical shell dynamos at varying Prandtl numbers

“…Earlier mean-field simulations of αΩ dynamos have suggested that solutions with a perfect conductor boundary condition are similar to those in full spherical shells (Jennings et al 1990). However, more recent work by Cole et al (2016) has demonstrated that this conclusion is not generally valid and depends on the nature of the solutions. Their work also suggests that the use of a normal field boundary condition at high latitudes might be a better way of obtaining solutions that are applicable to full spherical shells.…”