The dynamics of two interacting compositional plumes

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Abstract

The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied. The fluid within and outside the columns is thermally stably stratified and has a kinematic viscosity, ν, and a thermal diffusivity, K. The mean vertical flow and the associated temperature profiles depending on the horizontal coordinate normal to the surfaces of the columns are obtained and the associated buoyancy, heat and material fluxes are discussed. The stability of the mean state to infinitesimal disturbances is governed by the five dimensionless parameters: the number R (=UL/ν, where U and L are characteristic velocity and length, respectively) which measures the strength of the compositional buoyancy, x0, x1, d the dimensionless measures of the thickness of the two plumes and the distance between them, respectively, and G{cyrillic} representing the ratio of the strengths of the two plumes. The stability is examined for small values of R. The preferred mode of instability is studied in the space (x0, x1, d, G{cyrillic}). When a single plume is present (and x1, d, G{cyrillic} = 0), it is already known that the perturbations are neutral at O(R0) and linearly unstable at O(R1) for all values of x0 and Prandtl number, σ (=ν/κ). It is shown here that at O(R0), the presence of a second interacting plume has the significant effect that the system of two plumes becomes unstable for a certain range of the parameters while it remains neutrally stable for the others. In contrast with the instability of the single plume, the instability of the two interacting plumes does not depend, at the O(R0) level, on the Prandtl number of the fluid. However, the neutrally stable two plumes might suffer instability at O(R0) and that instability may depend on the Prandtl number. The instability is found to be driven by the gradients of all of the concentration of light material, the flow and temperature of the basic state. The presence of the second plume destroys the definite parity of the perturbations' solution and this can lead to non-zero total helicity.

Original languageEnglish
Pages (from-to)29-63
Number of pages35
JournalGeophysical and Astrophysical Fluid Dynamics
Volume104
Issue number1
DOIs
Publication statusPublished - Feb 2010

Fingerprint

plumes
plume
Prandtl number
Fluids
fluid
fluids
Buoyancy
buoyancy
perturbation
Thermal diffusivity
thermal diffusivity
temperature profile
temperature profiles
diffusivity
heat flux
parity
disturbances
Viscosity
kinematics
viscosity

Keywords

  • Earth's core
  • Helicity
  • Instability
  • Plumes

ASJC Scopus subject areas

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

Cite this

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title = "The dynamics of two interacting compositional plumes",
abstract = "The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied. The fluid within and outside the columns is thermally stably stratified and has a kinematic viscosity, ν, and a thermal diffusivity, K. The mean vertical flow and the associated temperature profiles depending on the horizontal coordinate normal to the surfaces of the columns are obtained and the associated buoyancy, heat and material fluxes are discussed. The stability of the mean state to infinitesimal disturbances is governed by the five dimensionless parameters: the number R (=UL/ν, where U and L are characteristic velocity and length, respectively) which measures the strength of the compositional buoyancy, x0, x1, d the dimensionless measures of the thickness of the two plumes and the distance between them, respectively, and G{cyrillic} representing the ratio of the strengths of the two plumes. The stability is examined for small values of R. The preferred mode of instability is studied in the space (x0, x1, d, G{cyrillic}). When a single plume is present (and x1, d, G{cyrillic} = 0), it is already known that the perturbations are neutral at O(R0) and linearly unstable at O(R1) for all values of x0 and Prandtl number, σ (=ν/κ). It is shown here that at O(R0), the presence of a second interacting plume has the significant effect that the system of two plumes becomes unstable for a certain range of the parameters while it remains neutrally stable for the others. In contrast with the instability of the single plume, the instability of the two interacting plumes does not depend, at the O(R0) level, on the Prandtl number of the fluid. However, the neutrally stable two plumes might suffer instability at O(R0) and that instability may depend on the Prandtl number. The instability is found to be driven by the gradients of all of the concentration of light material, the flow and temperature of the basic state. The presence of the second plume destroys the definite parity of the perturbations' solution and this can lead to non-zero total helicity.",
keywords = "Earth's core, Helicity, Instability, Plumes",
author = "Elbashir, {T. B A} and {Al Lawati}, {M. A.} and Eltayeb, {I. A.}",
year = "2010",
month = "2",
doi = "10.1080/03091920903255142",
language = "English",
volume = "104",
pages = "29--63",
journal = "Geophysical and Astrophysical Fluid Dynamics",
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TY - JOUR

T1 - The dynamics of two interacting compositional plumes

AU - Elbashir, T. B A

AU - Al Lawati, M. A.

AU - Eltayeb, I. A.

PY - 2010/2

Y1 - 2010/2

N2 - The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied. The fluid within and outside the columns is thermally stably stratified and has a kinematic viscosity, ν, and a thermal diffusivity, K. The mean vertical flow and the associated temperature profiles depending on the horizontal coordinate normal to the surfaces of the columns are obtained and the associated buoyancy, heat and material fluxes are discussed. The stability of the mean state to infinitesimal disturbances is governed by the five dimensionless parameters: the number R (=UL/ν, where U and L are characteristic velocity and length, respectively) which measures the strength of the compositional buoyancy, x0, x1, d the dimensionless measures of the thickness of the two plumes and the distance between them, respectively, and G{cyrillic} representing the ratio of the strengths of the two plumes. The stability is examined for small values of R. The preferred mode of instability is studied in the space (x0, x1, d, G{cyrillic}). When a single plume is present (and x1, d, G{cyrillic} = 0), it is already known that the perturbations are neutral at O(R0) and linearly unstable at O(R1) for all values of x0 and Prandtl number, σ (=ν/κ). It is shown here that at O(R0), the presence of a second interacting plume has the significant effect that the system of two plumes becomes unstable for a certain range of the parameters while it remains neutrally stable for the others. In contrast with the instability of the single plume, the instability of the two interacting plumes does not depend, at the O(R0) level, on the Prandtl number of the fluid. However, the neutrally stable two plumes might suffer instability at O(R0) and that instability may depend on the Prandtl number. The instability is found to be driven by the gradients of all of the concentration of light material, the flow and temperature of the basic state. The presence of the second plume destroys the definite parity of the perturbations' solution and this can lead to non-zero total helicity.

AB - The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied. The fluid within and outside the columns is thermally stably stratified and has a kinematic viscosity, ν, and a thermal diffusivity, K. The mean vertical flow and the associated temperature profiles depending on the horizontal coordinate normal to the surfaces of the columns are obtained and the associated buoyancy, heat and material fluxes are discussed. The stability of the mean state to infinitesimal disturbances is governed by the five dimensionless parameters: the number R (=UL/ν, where U and L are characteristic velocity and length, respectively) which measures the strength of the compositional buoyancy, x0, x1, d the dimensionless measures of the thickness of the two plumes and the distance between them, respectively, and G{cyrillic} representing the ratio of the strengths of the two plumes. The stability is examined for small values of R. The preferred mode of instability is studied in the space (x0, x1, d, G{cyrillic}). When a single plume is present (and x1, d, G{cyrillic} = 0), it is already known that the perturbations are neutral at O(R0) and linearly unstable at O(R1) for all values of x0 and Prandtl number, σ (=ν/κ). It is shown here that at O(R0), the presence of a second interacting plume has the significant effect that the system of two plumes becomes unstable for a certain range of the parameters while it remains neutrally stable for the others. In contrast with the instability of the single plume, the instability of the two interacting plumes does not depend, at the O(R0) level, on the Prandtl number of the fluid. However, the neutrally stable two plumes might suffer instability at O(R0) and that instability may depend on the Prandtl number. The instability is found to be driven by the gradients of all of the concentration of light material, the flow and temperature of the basic state. The presence of the second plume destroys the definite parity of the perturbations' solution and this can lead to non-zero total helicity.

KW - Earth's core

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KW - Instability

KW - Plumes

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