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, σ_m = ν/η, the Chandrasekhar number, Q _c, the Reynolds number, Re, and the ratios, B_v, 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, σ_m and B_v, 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.