### Abstract

A column of finite thickness containing compositionally buoyant fluid is found to rise in an infinite less buoyant fluid in the presence of uniform rotation and magnetic field. The fluids both within and outside the column have the same finite viscosity, ν, thermal diffusivity, κ and magnetic diffusivity, η. The stability of the column to harmonic disturbances of its interfaces, governed by five dimensionless parameters: the Taylor number, τ^{2} (which measures the ratio of Coriolis to viscous forces), the Chandrasekhar number, Qc (which measures the ratio of Lorenz to viscous forces), the thickness of the plume, x_{0}, the Reynolds number, Re (which here measures the strength of the forcing) and B_{z} and ω_{H} (which measure the inclinations of the ambient magnetic field and rotation vector to the vertical respectively), is studied. The order of the growth rate of the instability in terms of Re is determined by rotation. The column is unstable for all values of the parameters τ, Qc, χ_{0}, B_{z}, ω_{H} when Re is small. The instability is necessarily three-dimensional. It takes the form of a varicose or sinuous mode propagating at an angle to both field and rotation. The presence of the horizontal component of rotation tends to stabilize the system while that of the vertical field tends to destabilize it. The introduction of a magnetic field inclined to the vertical to an inclined rotation model can reverse the role of the horizontal component of rotation by making it enhance the instability. The dependence of the preference of the varicose and sinuous modes on the parameters of the system is illustrated in regime diagrams. The helicity and α-effect of the unstable motions are discussed briefly.

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

Pages (from-to) | 429-455 |

Number of pages | 27 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 100 |

Issue number | 4-5 |

DOIs | |

Publication status | Published - Aug 2006 |

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### Keywords

- Compositional plume
- Dynamo
- Instability
- Magnetic field
- Rotation

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Mechanics of Materials
- Computational Mechanics
- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

**The stability of a compositional plume rotating in the presence of a magnetic field.** / Eltayeb, I. A.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 100, no. 4-5, pp. 429-455. https://doi.org/10.1080/03091920600799541

}

TY - JOUR

T1 - The stability of a compositional plume rotating in the presence of a magnetic field

AU - Eltayeb, I. A.

PY - 2006/8

Y1 - 2006/8

N2 - A column of finite thickness containing compositionally buoyant fluid is found to rise in an infinite less buoyant fluid in the presence of uniform rotation and magnetic field. The fluids both within and outside the column have the same finite viscosity, ν, thermal diffusivity, κ and magnetic diffusivity, η. The stability of the column to harmonic disturbances of its interfaces, governed by five dimensionless parameters: the Taylor number, τ2 (which measures the ratio of Coriolis to viscous forces), the Chandrasekhar number, Qc (which measures the ratio of Lorenz to viscous forces), the thickness of the plume, x0, the Reynolds number, Re (which here measures the strength of the forcing) and Bz and ωH (which measure the inclinations of the ambient magnetic field and rotation vector to the vertical respectively), is studied. The order of the growth rate of the instability in terms of Re is determined by rotation. The column is unstable for all values of the parameters τ, Qc, χ0, Bz, ωH when Re is small. The instability is necessarily three-dimensional. It takes the form of a varicose or sinuous mode propagating at an angle to both field and rotation. The presence of the horizontal component of rotation tends to stabilize the system while that of the vertical field tends to destabilize it. The introduction of a magnetic field inclined to the vertical to an inclined rotation model can reverse the role of the horizontal component of rotation by making it enhance the instability. The dependence of the preference of the varicose and sinuous modes on the parameters of the system is illustrated in regime diagrams. The helicity and α-effect of the unstable motions are discussed briefly.

AB - A column of finite thickness containing compositionally buoyant fluid is found to rise in an infinite less buoyant fluid in the presence of uniform rotation and magnetic field. The fluids both within and outside the column have the same finite viscosity, ν, thermal diffusivity, κ and magnetic diffusivity, η. The stability of the column to harmonic disturbances of its interfaces, governed by five dimensionless parameters: the Taylor number, τ2 (which measures the ratio of Coriolis to viscous forces), the Chandrasekhar number, Qc (which measures the ratio of Lorenz to viscous forces), the thickness of the plume, x0, the Reynolds number, Re (which here measures the strength of the forcing) and Bz and ωH (which measure the inclinations of the ambient magnetic field and rotation vector to the vertical respectively), is studied. The order of the growth rate of the instability in terms of Re is determined by rotation. The column is unstable for all values of the parameters τ, Qc, χ0, Bz, ωH when Re is small. The instability is necessarily three-dimensional. It takes the form of a varicose or sinuous mode propagating at an angle to both field and rotation. The presence of the horizontal component of rotation tends to stabilize the system while that of the vertical field tends to destabilize it. The introduction of a magnetic field inclined to the vertical to an inclined rotation model can reverse the role of the horizontal component of rotation by making it enhance the instability. The dependence of the preference of the varicose and sinuous modes on the parameters of the system is illustrated in regime diagrams. The helicity and α-effect of the unstable motions are discussed briefly.

KW - Compositional plume

KW - Dynamo

KW - Instability

KW - Magnetic field

KW - Rotation

UR - http://www.scopus.com/inward/record.url?scp=33845523373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845523373&partnerID=8YFLogxK

U2 - 10.1080/03091920600799541

DO - 10.1080/03091920600799541

M3 - Article

AN - SCOPUS:33845523373

VL - 100

SP - 429

EP - 455

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 4-5

ER -