Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone

We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfvén speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer. In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior

Double-diffusive instabilities of a shear-generated magnetic layer

Previous theoretical work has speculated about the existence of double-diffusive magnetic buoyancy instabilities of a dynamically evolving horizontal magnetic layer generated by the interaction of forced vertically sheared velocity and a background vertical magnetic field. Here we confirm numerically that if the ratio of the magnetic to thermal diffusivities is sufficiently low then such instabilities can indeed exist, even for high Richardson number shear flows. Magnetic buoyancy may therefore occur via this mechanism for parameters that are likely to be relevant to the solar tachocline, where regular magnetic buoyancy instabilities are unlikely.Comment: Submitted to ApJ

The Evolution of a Double Diffusive Magnetic Buoyancy Instability

Recently, Silvers, Vasil, Brummell, & Proctor (2009), using numerical simulations, confirmed the existence of a double diffusive magnetic buoyancy instability of a layer of horizontal magnetic field produced by the interaction of a shear velocity field with a weak vertical field. Here, we demonstrate the longer term nonlinear evolution of such an instability in the simulations. We find that a quasi two-dimensional interchange instability rides (or "surfs") on the growing shear-induced background downstream field gradients. The region of activity expands since three-dimensional perturbations remain unstable in the wake of this upward-moving activity front, and so the three-dimensional nature becomes more noticeable with time.Comment: 9 pages; 3 figures; accepted to appear in IAU symposium 27

How can large-scale twisted magnetic structures naturally emerge from buoyancy instabilities?

We consider the three-dimensional instability of a layer of horizontal magnetic field in a polytropic atmosphere where, contrary to previous studies, the field lines in the initial state are not unidirectional. We show that if the twist is initially concentrated inside the unstable layer, the modifications of the instability reported by several authors (see e.g. Cattaneo et al. (1990)) are only observed when the calculation is restricted to two dimensions. In three dimensions, the usual interchange instability occurs, in the direction fixed by the field lines at the interface between the layer and the field-free region. We therefore introduce a new configuration: the instability now develops in a weakly magnetised atmosphere where the direction of the field can vary with respect to the direction of the strong unstable field below, the twist being now concentrated at the upper interface. Both linear stability analysis and non-linear direct numerical simulations are used to study this configuration. We show that from the small-scale interchange instability, large-scale twisted coherent magnetic structures are spontaneously formed, with possible implications to the formation of active regions from a deep-seated solar magnetic field

Interactions between magnetohydrodynamic shear instabilities and convective flows in the solar interior

Motivated by the interface model for the solar dynamo, this paper explores the complex magnetohydrodynamic interactions between convective flows and shear-driven instabilities. Initially, we consider the dynamics of a forced shear flow across a convectively-stable polytropic layer, in the presence of a vertical magnetic field. When the imposed magnetic field is weak, the dynamics are dominated by a shear flow (Kelvin-Helmholtz type) instability. For stronger fields, a magnetic buoyancy instability is preferred. If this stably stratified shear layer lies below a convectively unstable region, these two regions can interact. Once again, when the imposed field is very weak, the dynamical effects of the magnetic field are negligible and the interactions between the shear layer and the convective layer are relatively minor. However, if the magnetic field is strong enough to favour magnetic buoyancy instabilities in the shear layer, extended magnetic flux concentrations form and rise into the convective layer. These magnetic structures have a highly disruptive effect upon the convective motions in the upper layer.Comment: 11 pages, 10 figures, accepted for publication in MNRA