A Bibliography of Partially Solidified Systems

Loper, David E.

doi:10.1007/978-94-009-3587-7_23

Cited by 6 publications

(7 citation statements)

References 355 publications

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“…The study of convective motions driven by the energy released by the solidification of a component of a fluid alloy has received considerable attention recently because of its relevance to many industrial and geophysical applications (see e.g. Copley et al 1970;Loper 1978Loper , 1983Loper , 1987Loper & Roberts 1981Davis 1990;Huppert 1990;Tait & Jaupart 1992;Worster 1992). When a twocomponent fluid melt, with the heavier component having the higher melting point, is chilled from below the heavy component solidifies first and settles at the bottom of the container (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Compositional convection in the presence of rotation

Eltayeb¹,

Hamza

1998

J. Fluid Mech.

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The stability of a compositionally buoyant plume, of circular cross-section, rising in a rotating infinite fluid is investigated. Both plume and fluid have the same non-zero kinematic viscosity, ν, and thermal diffusivity, κ. The growth rate of the instability depends on the Taylor number, Ta (which is a dimensionless number measuring the effect of the Coriolis force relative to the viscous force) and on the thickness, s0, of the plume in addition to the Prandtl number, σ(=ν/κ) and the Reynolds number, R (which measures the strength of the forcing). The analysis is restricted to the case of small R. It is found that the presence of rotation enhances instability. A simple model of a single interface separating the two parts of an infinite fluid is investigated first in order to isolate the mechanism responsible for the increase in the growth rate with rotation. It is shown that the Coriolis force interacts with the zonal velocity component to produce a velocity component normal to the interface. For the right choice of wave vector components, this normal velocity component is in phase with the displacement of the interface and this leads to instability. The maximum growth rate is identified in the whole space of the parameters σ, Ta, s0 when R[Lt ]1. While the maximum growth rate is of order R2 in the absence of rotation, it is increased to order R in the presence of rotation. It is also found that the Prandtl number, σ, which has a strong influence on the growth rate in the absence of rotation, plays a subservient role when rotation is present.

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Section: Introductionmentioning

confidence: 99%

Compositional convection in the presence of rotation

Eltayeb¹,

Hamza

1998

J. Fluid Mech.

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“…The mushy layer in the absence of rotation and magnetic fields has been of interest to metallurgists due to its relevance to iron casting and crystal growth, particularly after the visual illustrations of the experiments carried out by Copley et al (1970). More recently it has been of interest to geophysics also (Gubbins 1977, Loper 1978, 1987, Jellinek et al 1999, Shimizu et al 2005. Studies of mushy layers have shown that they suffer morphological instabilities which lead to the formation of thin filaments of light fluid material rising from the mush into the overlying melt (Worster 1997).…”

Section: Introductionmentioning

confidence: 97%

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

Eltayeb

2006

Geophysical & Astrophysical Fluid Dynamics

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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, , thermal diffusivity, and magnetic diffusivity, . The stability of the column to harmonic disturbances of its interfaces, governed by five dimensionless parameters: the Taylor number, 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 ! 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 , Qc, x 0 , B z , ! 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 -effect of the unstable motions are discussed briefly.

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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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A Bibliography of Partially Solidified Systems

Cited by 6 publications

References 355 publications

Compositional convection in the presence of rotation

Compositional convection in the presence of rotation

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

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

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