Abstract
Linear stability theory is applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine values of the Marangoni number above which instability is guaranteed. In an earlier work energy theory results had been presented. They yield Marangoni numbers below which the convection is stable under arbitrary perturbations. The least-stable mode in these results was never an axisymmetric one. Here, first results on the most unstable modes will be reported and the numerical procedure employed will be described in detail. Our results indicate that the instability is due to a subcritical Hopf bifurcationwhich breaks the axisymmetry of the basic state.
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© 1992 Birkhäuser Verlag Basel
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Mittelmann, H.D., Chang, KT., Jankowski, D.F., Neitzel, G.P. (1992). Linear Stability of Axisymmetric Thermocapillary Convection in Crystal Growth. In: Allgower, E.L., Böhmer, K., Golubitsky, M. (eds) Bifurcation and Symmetry. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 104. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7536-3_24
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DOI: https://doi.org/10.1007/978-3-0348-7536-3_24
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