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.