### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- General

### 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

**Compositional convection in the presence of a magnetic field. I. A single interface.** / Eltayeb, I. A.; Hamza, E. A.; Jervase, J. A.; Krishnan, E.; Loper, D. E.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 460, no. 2052, pp. 3505-3528. https://doi.org/10.1098/rspa.2004.1375

}

TY - JOUR

T1 - Compositional convection in the presence of a magnetic field. I. A single interface

AU - Eltayeb, I. A.

AU - Hamza, E. A.

AU - Jervase, J. A.

AU - Krishnan, E.

AU - Loper, D. E.

PY - 2004/12/8

Y1 - 2004/12/8

N2 - 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, Q c, 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.

AB - 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, Q c, 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.

KW - α-effect

KW - Compositional convection

KW - Compositional plumes

KW - Geodynamo

KW - Helicity

KW - Hydromagnetic stability

UR - http://www.scopus.com/inward/record.url?scp=17144391056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17144391056&partnerID=8YFLogxK

U2 - 10.1098/rspa.2004.1375

DO - 10.1098/rspa.2004.1375

M3 - Article

VL - 460

SP - 3505

EP - 3528

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

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

SN - 0080-4630

IS - 2052

ER -