Blob instability in rotating compositional convection

Claßen, Sabine; Heimpel, Moritz; Christensen, Ulrich R.

doi:10.1029/1998gl900227

Cited by 17 publications

(18 citation statements)

References 14 publications

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“…However, it is likely that any such plume is unstable (e.g., see Eltayeb and Loper, 1997;Classen et al, 1999;Eltayeb et al, 2005), leading to the production of a sequence of plumes governed by the equations presented above. However, it is likely that any such plume is unstable (e.g., see Eltayeb and Loper, 1997;Classen et al, 1999;Eltayeb et al, 2005), leading to the production of a sequence of plumes governed by the equations presented above.…”

Section: Scaling and Structure Of Plumesmentioning

confidence: 99%

Turbulence and Small-Scale Dynamics in the Core

Loper

2007

Treatise on Geophysics

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Section: Scaling and Structure Of Plumesmentioning

confidence: 99%

Turbulence and Small-Scale Dynamics in the Core

Loper

2007

Treatise on Geophysics

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“…The study of fluid motions induced during the directional solidification of fluid alloys has received considerable attention over the past four decades (Copley et al 1970, Loper 1978, Huppert and Worster 1985, Loper 1987, Huppert 1988, 1990, Worster 1992, 1997, Hellawell et al 1993, Eltayeb and Loper 1994, 1997, Eltayeb and Hamza, 1998, Eltayeb 1999, Jellinek et al 1999, Classen et al 1999, Morse 2000, Eltayeb et al 2004, 2005 (hereinafter referred to as EHJKL), Eltayeb 2006). These studies include theoretical and experimental investigations relating to diverse applications ranging from metallurgy to geophysics.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of two interacting compositional plumes in the presence of a magnetic field

Al‐Lawatia

El-Bashir

Eltayeb

et al. 2011

Geophysical & Astrophysical Fluid Dynamics

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The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied in the presence of a uniform magnetic field, B 0 . The fluid is thermally stably stratified and has a viscosity, , a thermal diffusivity, and magnetic diffusivity, . The stability of the mean state to infinitesimal disturbances is governed by the seven dimensionless parameters: the Reynolds number, R (¼UL/, where U, L are characteristic velocity and length respectively) which measures the strength of the compositional buoyancy; the dimensionless measures x 0 , x 1 , d of the thickness of the two plumes and the distance between them, respectively; the ratio À of the strengths of the two plumes (as measured by their basic concentration of light material); the Chandrasekhar number, Qc (¼B 2 0 L 2 = 0 , in which is the magnetic permeability, 0 the fluid density and B 0 a characteristic unit of magnetic field), is a measure of the magnitude of the magnetic field and the normalized horizontal projection B H ¼ sin of the magnetic field, where measures the inclination of the magnetic field to the vertical. The stability is examined for small values of R. The preferred mode of instability is studied in the parameter space (x 0 , x 1 , d, À, Qc,B H ). It is shown that the influence of the magnetic field does not change the order of the magnitude of the growth rate from O(R 0 ) of the two non-magnetic interacting plumes and it does not introduce any new modes to the stability problem. However, the presence of the magnetic field introduces novel features to the stability problem. For any fixed set x 0 , x 1 , d, À, Qc, the growth rate can either increase withB H or initially decrease reaching a minimum before it increases again. As Qc increases, with x 0 , x 1 , d, À,B H fixed, the growth rate can assume one of four different behaviours: (i) it maintains the same value of the non-magnetic case with the disturbance propagating along field lines; (ii) it decreases steadily with Qc; (iii) it maintains the same value as in the absence of the field until a value Qcmðx 0 , x 1 , d, À,B H Þ is reached when it starts to increase to a maximum before it decreases to zero for large values of Qc and (iv) it increases from its value for Qc ¼ 0 reaching a maximum before it decreases steadily to zero at some value of Qc dependent on the other parameters. The helicity and -effect have also been studied to find that the unstable motions can produce mean helicity and -effect.

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“…The study by Eltayeb and Hamza (1998) on the stability of a vertically rotating cylindrical plume of circular cross-section showed that the presence of rotation increased the growth rate by an order of magnitude, from O(R) in the absence of rotation to O(1) when rotation is present. Classen et al (1999) studied experimentally plumes rising from a mushy layer in a vertically rotating fluid to find that the plumes are bent by the rotation and break up into blobs. Noting that stability properties of a Cartesian plume are qualitatively similar to those of a cylindrical plume of circular cross-section in similar surroundings, Elbashir et al (2010) studied the stability of two interacting Cartesian plumes to find that they possess a growth rate of O(1) on the convective time scale.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, a number of publications have addressed the dynamics of compositional plumes (see, e.g. Eltayeb and Loper 1997, Classen et al 1999, Eltayeb 2006. Eltayeb and Loper (1991, 1994, 1997 studied the stability of compositional plumes rising in a fluid of infinite extent to find that a plume is always linearly unstable for all non-zero Grashoff numbers, R, where the Grashoff number is the ratio of buoyancy to viscous forces.…”

Section: Introductionmentioning

confidence: 99%

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

Eltayeb

El-Bashir

2014

Geophysical & Astrophysical Fluid Dynamics

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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, between the rotation vector and the vertical, the concentration strength Γ , of the second plume relative to that of the first, the thicknesses, x 0 , x 1 , 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 x 0 , x 1 , d, R, ω z (=cos φ), the growth rate increases with τ to a finite value as τ 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.

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Blob instability in rotating compositional convection

Cited by 17 publications

References 14 publications

Turbulence and Small-Scale Dynamics in the Core

Turbulence and Small-Scale Dynamics in the Core

The dynamics of two interacting compositional plumes in the presence of a magnetic field

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

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