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Please use this identifier to cite this item:
http://hdl.handle.net/2142/988
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| Title: |
On nonlinear convection in mushy layers. Part 2: Mixed oscillatory and stationary modes of convection |
| Authors: |
Riahi, Daniel N. |
| Keywords: |
Nonlinear convection |
| Issue Date: |
2004 |
| Publisher: |
Cambridge University Press |
| Citation Information: |
Daniel N. Riahi. On nonlinear convection in mushy layers: Part 2. Mixed oscillatory and stationary modes of convection. Journal of Fluid Mechanics, Vol. 517, 2004, pp.71- 101. |
| Abstract / Summary: |
This paper presents part 2 of a study of nonlinear convection in horizontal mushy
layers during the solidification of binary alloys. Part 1 dealt with only the oscillatory
modes of convection (Riahi, J. Fluid Mech. vol. 467, 2002, pp. 331–359). In the present
paper we consider the particular range of parameters where the critical values of the
scaled Rayleigh number R for the onset of oscillatory and stationary convection are
close to each other, and we develop and analyse a nonlinear theory in such a parameter
regime which takes into account those mixed stationary and oscillatory modes of
convection with common wavenumber vectors. Under a near-eutectic approximation
and in the limit of large far-field temperature, we first determine a number of weakly
nonlinear solutions, and then the stability of these solutions is investigated. The most
interesting result is the preference for a mixed solution composed of standing and
stationary hexagonal modes over a relatively wide range of the parameter values and
for R just above its lowest subcritical value where convection is possible. Such a
preferred solution has properties mostly in agreement with the experimental results
due to Tait et al. (Nature, vol. 359, 1992, pp. 406–408) in the sense that the flow
is downward at the cell centres, upward at the cell boundaries and there is some
tendency for channel formation at the cell nodes. |
| URI: |
http://hdl.handle.net/2142/988 |
| DOI: |
10.1017/S0022112004000849 |
| Type of Resource: |
text |
| Genre of Resource: |
article |
| Publication Status: |
published or submitted for publication |
| Peer-Reviewed: |
is peer reviewed |
| Appears in Collections: |
Theoretical and Applied Mechanics (TAM) Published Papers
|
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