### Abstract

The analysis of part I, dealing with the morphological instability of a single interface in a fluid of infinite extent, is extended to the case of a Cartesian plume of compositionally buoyant fluid, of thickness 2x_{0}, enclosed between two vertical interfaces. The problem depends on six dimensionless parameters: the Prandtl number, ó; the magnetic Prandtl number, ś_{m}; the Chandrasekhar number, Q_{c}; the Reynolds number, Re; the ratio, Bv, of vertical to horizontal components of the ambient magnetic field and the dimensionless plume thickness. Attention is focused on the preferred mode of instability, which occurs in the limit Re«/1 for all values of the parameters. This mode can be either sinuous or varicose with the wavenumber vector either vertical or oblique, comprising four types. The regions of preference of these four modes are represented in regime diagrams in the (x0, ó) plane for different values of ó_{m}, Q_{c}, B_{v}. These regions are strongly dependent on the field inclination and field strength and, to a lesser extent, on magnetic diffusion. The overall maximum growth rate for any prescribed set of the parameters ó_{m}, Q_{c}, B_{v}, occurs when 1.3«x_{0} «1.7, and is sinuous for small ó and varicose for large ó. The magnetic field can enhance instability for a certain range of thickness of the plume. The enhancement of instability is due to the interaction of the field with viscous diffusion resulting in a reverse role for viscosity. The dependence of the helicity and α-effect on the parameters is also discussed.

Original language | English |
---|---|

Pages (from-to) | 2605-2633 |

Number of pages | 29 |

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

Volume | 461 |

Issue number | 2060 |

DOIs | |

Publication status | Published - Aug 5 2005 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)
- Mathematics(all)
- Physics and Astronomy(all)

### Cite this

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

*461*(2060), 2605-2633. https://doi.org/10.1098/rspa.2005.1473

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

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 461, no. 2060, pp. 2605-2633. https://doi.org/10.1098/rspa.2005.1473

}

TY - JOUR

T1 - Compositional convection in the presence of a magnetic field. Ii. Cartesian plume

AU - Eltayeb, I. A.

AU - Hamza, E. A.

AU - Jervase, J. A.

AU - Krishnan, E. V.

AU - Loper, D. E.

PY - 2005/8/5

Y1 - 2005/8/5

N2 - The analysis of part I, dealing with the morphological instability of a single interface in a fluid of infinite extent, is extended to the case of a Cartesian plume of compositionally buoyant fluid, of thickness 2x0, enclosed between two vertical interfaces. The problem depends on six dimensionless parameters: the Prandtl number, ó; the magnetic Prandtl number, śm; the Chandrasekhar number, Qc; the Reynolds number, Re; the ratio, Bv, of vertical to horizontal components of the ambient magnetic field and the dimensionless plume thickness. Attention is focused on the preferred mode of instability, which occurs in the limit Re«/1 for all values of the parameters. This mode can be either sinuous or varicose with the wavenumber vector either vertical or oblique, comprising four types. The regions of preference of these four modes are represented in regime diagrams in the (x0, ó) plane for different values of óm, Qc, Bv. These regions are strongly dependent on the field inclination and field strength and, to a lesser extent, on magnetic diffusion. The overall maximum growth rate for any prescribed set of the parameters óm, Qc, Bv, occurs when 1.3«x0 «1.7, and is sinuous for small ó and varicose for large ó. The magnetic field can enhance instability for a certain range of thickness of the plume. The enhancement of instability is due to the interaction of the field with viscous diffusion resulting in a reverse role for viscosity. The dependence of the helicity and α-effect on the parameters is also discussed.

AB - The analysis of part I, dealing with the morphological instability of a single interface in a fluid of infinite extent, is extended to the case of a Cartesian plume of compositionally buoyant fluid, of thickness 2x0, enclosed between two vertical interfaces. The problem depends on six dimensionless parameters: the Prandtl number, ó; the magnetic Prandtl number, śm; the Chandrasekhar number, Qc; the Reynolds number, Re; the ratio, Bv, of vertical to horizontal components of the ambient magnetic field and the dimensionless plume thickness. Attention is focused on the preferred mode of instability, which occurs in the limit Re«/1 for all values of the parameters. This mode can be either sinuous or varicose with the wavenumber vector either vertical or oblique, comprising four types. The regions of preference of these four modes are represented in regime diagrams in the (x0, ó) plane for different values of óm, Qc, Bv. These regions are strongly dependent on the field inclination and field strength and, to a lesser extent, on magnetic diffusion. The overall maximum growth rate for any prescribed set of the parameters óm, Qc, Bv, occurs when 1.3«x0 «1.7, and is sinuous for small ó and varicose for large ó. The magnetic field can enhance instability for a certain range of thickness of the plume. The enhancement of instability is due to the interaction of the field with viscous diffusion resulting in a reverse role for viscosity. The dependence of the helicity and α-effect on the parameters is also discussed.

KW - Compositional convection

KW - Compositional plumes

KW - Geodynamo

KW - Helicity

KW - Hydromagnetic stability

UR - http://www.scopus.com/inward/record.url?scp=33845542918&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845542918&partnerID=8YFLogxK

U2 - 10.1098/rspa.2005.1473

DO - 10.1098/rspa.2005.1473

M3 - Article

AN - SCOPUS:33845542918

VL - 461

SP - 2605

EP - 2633

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 - 2060

ER -