Abstract
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.
Original language | English (US) |
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Pages (from-to) | 518-528 |
Number of pages | 11 |
Journal | Journal of fluid Mechanics |
Volume | 675 |
DOIs | |
State | Published - May 25 2011 |
Keywords
- convection in porous media
- low-dimensional models
- solidification/melting
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering