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

I. A. Eltayeb, E. A. Hamza, J. A. Jervase, E. V. Krishnan, D. E. Loper

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)2605-2633
Number of pages29
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume461
Issue number2060
DOIs
Publication statusPublished - Aug 5 2005

Fingerprint

Cartesian
plumes
Convection
convection
Magnetic Field
Magnetic fields
Vertical
Prandtl number
magnetic fields
Dimensionless
magnetic diffusion
Fluid
Fluids
Helicity
fluids
Inclination
Oblique
inclination
Reynolds number
Reverse

Keywords

  • Compositional convection
  • Compositional plumes
  • Geodynamo
  • Helicity
  • Hydromagnetic stability

ASJC Scopus subject areas

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

Cite this

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title = "Compositional convection in the presence of a magnetic field. Ii. Cartesian plume",
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 2x0, enclosed between two vertical interfaces. The problem depends on six dimensionless parameters: the Prandtl number, {\'o}; 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, {\'o}) plane for different values of {\'o}m, 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 {\'o}m, Qc, Bv, occurs when 1.3«x0 «1.7, and is sinuous for small {\'o} and varicose for large {\'o}. 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.",
keywords = "Compositional convection, Compositional plumes, Geodynamo, Helicity, Hydromagnetic stability",
author = "Eltayeb, {I. A.} and Hamza, {E. A.} and Jervase, {J. A.} and Krishnan, {E. V.} and Loper, {D. E.}",
year = "2005",
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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

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U2 - 10.1098/rspa.2005.1473

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