Institute of Fundamental Technological Research

We revisit the problem introduced by Gilman (1970) and Acheson (1979) of linear stability of a plane layer of compressible fluid permeated by a horizontal magnetic field of magnitude decreasing with height with respect to short-wavelength two-dimensional perturbations varying in the directions perpendicular to the applied field. We show, that in the limit of large horizontal wave numbers the perturbations become strongly localised in the vertical direction. The motiavtion for this study is of astrophysical nature and comes from the common belief, that the magnetic buoyancy effects produce short-wavelength instabilities in the solar tachocline. We analyse the solar tachocline parameter regime to speculate about the strength of the magnetic field at the base of the solar convective zone and the time scales of the field variations induced by the magnetic buoyancy instability on the Sun.