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

Abstract

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.