The stability of two interacting compositional plumes under the influence of inclined rotation

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Abstract

The linear stability of two interacting compositional plumes rotating uniformly about an axis inclined to the vertical is studied. The problem is governed by seven dimensionless parameters: The Grashoff number, R, measuring the buoyancy force relative to the viscous force, the rotation parameter, τ, which measures the Coriolis force relative to the viscous force, the angle, φ{symbol}, between the rotation vector and the vertical, the concentration strength, of the second plume relative to that of the first, the thicknesses, x0, x1, of the two plumes and the distance, d, between them (which have been made dimensionless using the salt-finger length scale). It is shown that rotation destabilises the neutral modes present in its absence. For a given set of the parameters x0, x1, d, R, wz (=cosφ{symbol}), the growth rate increases with to a finite value as approaches infinity. The inclination of rotation to the horizontal is found to tend to stabilise a vertically rotating plume but succeeds only in reducing the magnitude of the growth rate while the order of magnitude remains the same. The introduction of a horizontal component of rotation also has a similar stabilising effect. The presence of a horizontal component of rotation also introduces a new mode which propagates horizontally across the vertical basic flow, provided the second plume acquires certain strength. The growth rate is of the same order of magnitude even when the rotation parameter increases indefinitely whatever values the other parameters take. The helicity of the unstable modes can take positive or negative values depending, in a complicated way, on the parameters. The helicity of the horizontally propagating wave is zero.

Original languageEnglish
Pages (from-to)437-462
Number of pages26
JournalGeophysical and Astrophysical Fluid Dynamics
Volume108
Issue number4
DOIs
Publication statusPublished - 2014

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plumes
plume
Coriolis force
Buoyancy
buoyancy
parameter
Salts
infinity
inclination
salt
salts

Keywords

  • Compositional plumes
  • Helicity
  • Rotation
  • Stability

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Mechanics of Materials
  • Computational Mechanics
  • Astronomy and Astrophysics

Cite this

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title = "The stability of two interacting compositional plumes under the influence of inclined rotation",
abstract = "The linear stability of two interacting compositional plumes rotating uniformly about an axis inclined to the vertical is studied. The problem is governed by seven dimensionless parameters: The Grashoff number, R, measuring the buoyancy force relative to the viscous force, the rotation parameter, τ, which measures the Coriolis force relative to the viscous force, the angle, φ{symbol}, between the rotation vector and the vertical, the concentration strength, of the second plume relative to that of the first, the thicknesses, x0, x1, of the two plumes and the distance, d, between them (which have been made dimensionless using the salt-finger length scale). It is shown that rotation destabilises the neutral modes present in its absence. For a given set of the parameters x0, x1, d, R, wz (=cosφ{symbol}), the growth rate increases with to a finite value as approaches infinity. The inclination of rotation to the horizontal is found to tend to stabilise a vertically rotating plume but succeeds only in reducing the magnitude of the growth rate while the order of magnitude remains the same. The introduction of a horizontal component of rotation also has a similar stabilising effect. The presence of a horizontal component of rotation also introduces a new mode which propagates horizontally across the vertical basic flow, provided the second plume acquires certain strength. The growth rate is of the same order of magnitude even when the rotation parameter increases indefinitely whatever values the other parameters take. The helicity of the unstable modes can take positive or negative values depending, in a complicated way, on the parameters. The helicity of the horizontally propagating wave is zero.",
keywords = "Compositional plumes, Helicity, Rotation, Stability",
author = "Eltayeb, {I. A.} and Elbashir, {T. B A}",
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AU - Eltayeb, I. A.

AU - Elbashir, T. B A

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N2 - The linear stability of two interacting compositional plumes rotating uniformly about an axis inclined to the vertical is studied. The problem is governed by seven dimensionless parameters: The Grashoff number, R, measuring the buoyancy force relative to the viscous force, the rotation parameter, τ, which measures the Coriolis force relative to the viscous force, the angle, φ{symbol}, between the rotation vector and the vertical, the concentration strength, of the second plume relative to that of the first, the thicknesses, x0, x1, of the two plumes and the distance, d, between them (which have been made dimensionless using the salt-finger length scale). It is shown that rotation destabilises the neutral modes present in its absence. For a given set of the parameters x0, x1, d, R, wz (=cosφ{symbol}), the growth rate increases with to a finite value as approaches infinity. The inclination of rotation to the horizontal is found to tend to stabilise a vertically rotating plume but succeeds only in reducing the magnitude of the growth rate while the order of magnitude remains the same. The introduction of a horizontal component of rotation also has a similar stabilising effect. The presence of a horizontal component of rotation also introduces a new mode which propagates horizontally across the vertical basic flow, provided the second plume acquires certain strength. The growth rate is of the same order of magnitude even when the rotation parameter increases indefinitely whatever values the other parameters take. The helicity of the unstable modes can take positive or negative values depending, in a complicated way, on the parameters. The helicity of the horizontally propagating wave is zero.

AB - The linear stability of two interacting compositional plumes rotating uniformly about an axis inclined to the vertical is studied. The problem is governed by seven dimensionless parameters: The Grashoff number, R, measuring the buoyancy force relative to the viscous force, the rotation parameter, τ, which measures the Coriolis force relative to the viscous force, the angle, φ{symbol}, between the rotation vector and the vertical, the concentration strength, of the second plume relative to that of the first, the thicknesses, x0, x1, of the two plumes and the distance, d, between them (which have been made dimensionless using the salt-finger length scale). It is shown that rotation destabilises the neutral modes present in its absence. For a given set of the parameters x0, x1, d, R, wz (=cosφ{symbol}), the growth rate increases with to a finite value as approaches infinity. The inclination of rotation to the horizontal is found to tend to stabilise a vertically rotating plume but succeeds only in reducing the magnitude of the growth rate while the order of magnitude remains the same. The introduction of a horizontal component of rotation also has a similar stabilising effect. The presence of a horizontal component of rotation also introduces a new mode which propagates horizontally across the vertical basic flow, provided the second plume acquires certain strength. The growth rate is of the same order of magnitude even when the rotation parameter increases indefinitely whatever values the other parameters take. The helicity of the unstable modes can take positive or negative values depending, in a complicated way, on the parameters. The helicity of the horizontally propagating wave is zero.

KW - Compositional plumes

KW - Helicity

KW - Rotation

KW - Stability

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