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Coupled convective and morphological instability in a simple model of the solidification of a binary alloy, including a shear flow

Published online by Cambridge University Press:  26 April 2006

S. A. Forth  and
A. A. Wheeler
S. A. Forth
Affiliation:
School of Mathematics, University Walk, Bristol, BS8 1TW, UK Present address: British Aerospace, Sowerby Research Centre, FPC 266, PO Box 5, Filton, Bristol, UK.
A. A. Wheeler
Affiliation:
School of Mathematics, University Walk, Bristol, BS8 1TW, UK
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Abstract

In this paper we provide a detailed description of the interaction of solutal convection and morphological instability in the presence of a model boundary-layer flow. We present a detailed investigation of the structure of the marginal surfaces in Rayleigh-number, Sekerka-number, Reynolds-number space associated with a linear stability analysis. We give mathematical arguments and physical mechanisms to explain the results and present a coherent description of this complicated situation. We identify two new modes, one convective and one morphological. We show that the oscillatory so-called ‘mixed’ modes that result from the coupling of morphological and convective modes play a central role in the unfolding of the solution structure by the shear flow. This flow has the effect of decoupling the convective and morphological modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 61 - 94
Copyright
© 1992 Cambridge University Press

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