Localisation of convection in mushy layers by weak background flow

It is known that freckles form at the sidewalls of directionally solidified materials. We present a weakly nonlinear analysis of the effects of a weak and slowly varying background flow formed by non-axial thermal gradients on convection near onset in a mushy layer. We find that in the two-dimension...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 675; pp. 518 - 528
Main Authors ROPER, S. M., DAVIS, S. H., VOORHEES, P. W.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 25.05.2011
Subjects
Computational fluid dynamics
Confining
Convection
Cross-disciplinary physics: materials science; rheology
Disturbances
Evolution
Exact sciences and technology
Flow control
Fluid mechanics
Materials science
Mathematical analysis
Phase diagrams and microstructures developed by solidification and solid-solid phase transformations
Physics
Porous materials
Solidification
Thermodynamics
Three dimensional
Walls
convection in porous media
low-dimensional models
solidification/melting
Modelling
Mushy zone
Directional solidification
Localization
Temperature gradients
Convection
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Summary:It is known that freckles form at the sidewalls of directionally solidified materials. We present a weakly nonlinear analysis of the effects of a weak and slowly varying background flow formed by non-axial thermal gradients on convection near onset in a mushy layer. We find that in the two-dimensional case, the onset of mush convection occurs away from the walls. However if three-dimensional disturbances are allowed, the onset occurs near the walls of the container confining the mush. We derive amplitude equations governing this behaviour and simulate their evolution numerically.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2011.117