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.Key words: convection -instabilities -MHD -Sun: interior -Sun: magnetic fields.
I N T RO D U C T I O NThe 11 year solar magnetic cycle is driven by a hydromagnetic dynamo. However, the exact nature of this dynamo mechanism is still not fully understood, and there are several scenarios that seek to explain the observed behaviour. The well-known 'interface' dynamo model (Parker 1993) is based on the idea that the dynamo operates in a region that straddles the base of the solar convection zone and the stably stratified region that lies beneath (for some recent reviews see Ossendrijver 2003;Proctor 2006; Dormy & Soward 2007;Silvers 2008). Although this is a conceptually appealing model for the solar dynamo, the only numerical investigations of the interface dynamo have been based upon mean-field dynamo theory (see e.g. Charbonneau & MacGregor 1997;Chan et al. 2004;Zhang, Liao & Schubert 2004;Bushby 2006). In mean-field theory, several aspects of the dynamo model (particularly the effects of turbulent convection) are parametrized. However, the resulting coefficients are poorly determined by both theory and observations. Due to the involved computational costs, it has not yet been possible to demonstrate the operation of the interface dynamo by carrying out threedimensional simulations of compressible magnetohydrodynamics. Given these computational constraints, it makes sense to investigate different components of the interface dynamo in isolation.