The influence of velocity shear on magnetic buoyancy instability in the solar tachocline

The Sun's large-scale magnetic field is believed to be generated deep within the Sun, at the base of the convection zone, in a predominantly stably stratified region of strong radial shear, known as the tachocline. Observations indicate that, owing to magnetic buoyancy, this field rises to the surface to form active regions with systematic properties. Whereas previous investigations of magnetic buoyancy instability have generally assumed a static basic state, here we investigate the role of an aligned shear in modifying this instability. We adopt two complementary approaches. Using the energy principle, we derive sufficient conditions for the stability of a magnetic field in a stratified, compressible shear flow. To investigate the nature of the unstable modes, we have performed a series of numerical calculations; these suggest that the shear has an "axisymmetrizing'' and stabilizing effect on the magnetic buoyancy instability. We discuss the implications for the instability of the solar magnetic field.