### 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.

Original language | English |
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Pages (from-to) | 3505-3528 |

Number of pages | 24 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 460 |

Issue number | 2052 |

DOIs | |

Publication status | Published - Dec 8 2004 |

### Keywords

- α-effect
- Compositional convection
- Compositional plumes
- Geodynamo
- Helicity
- Hydromagnetic stability

### ASJC Scopus subject areas

- General

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## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*460*(2052), 3505-3528. https://doi.org/10.1098/rspa.2004.1375