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Hydrodynamical instabilities of thermocapillary flow in a half-zone

Published online by Cambridge University Press:  26 April 2006

Måarten Levenstam  and
Gustav Amberg
Måarten Levenstam
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden Present address: Department of Mathematics, Chalmers University of Technology, S-411 22 Göteborg, Sweden.
Gustav Amberg
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
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Abstract

The stability of the flow in a half-zone configuration is analysed with the aid of direct numerical simulation. The work is concentrated on the small Prandtl numbers relevant for typical semiconductor melts. The axisymmetric thermocapillary flow is found to be unstable to a steady non-axisymmetric state with azimuthal wavenumber 2, for a zone with aspect ratio 1. The critical Reynolds number for this bifurcation is 1960. This three dimensional steady solution loses stability to an oscillatory state at a Reynolds number of 6250. For small Prandtl numbers, both bifurcations are seen to be quite insensitive to changes in the Prandtl number, and are thus hydrodynamic in nature. An analogy to the instability of thin vortex rings is made. This analogy suggests a physical mechanism behind the instability and also gives an explanation of how the azimuthal wavenumber of the bifurcated solution is selected. The implications of this for the floating-zone crystal growth process are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 357 - 372
Copyright
© 1995 Cambridge University Press

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