Compositional convection in the presence of a magnetic field. I. A single interface

We investigate the stability of a vertical interface separating two semi–infinite fluids with differing composition of light material and permeated by a magnetic field. Both fluids possess finite kinematic viscosity, ν, thermal diffusivity, κ, magnetic diffusivity, η, and negligible material diffusion. The stability depends on six dimensionless parameters: the Prandtl number, σ (where σ = ν/ κ), the magnetic Prandtl number, σm = ν/η, the Chandrasekhar number, Qc, the Reynolds number, Re, and the ratios, Bv, Γ of the vertical and normal components to the lateral component of field. A comprehensive study of the dependence of the stability on the parameters is made when Re is small. The presence of a horizontal magnetic field tends to reduce the growth rate of the non–magnetic modes and can also give rise to new modes of instability. The addition of a vertical component of field can completely counteract the stabilizing influence of the horizontal component. For field strengths in excess of some value dependent on σ, σm and Bv, the non–magnetic unstable mode is replaced by one of two magnetic modes, one of which is a roll aligned with the field and the other inclined to it. The helicity and α–effect of the small–scale unstable motions are also discussed.