Morphological instability of similarity solution to the Stefan problem with undercooling and surface tension

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Abstract

This paper concerns morphological stability of a similarity solution to the Stefan problem with surface tension and initial supercooling. The linear stability analysis shows that for a nonzero surface tension each perturbation mode with a nonzero wave number is stable. However, the solution is unstable with respect to perturbations with a zero wave number limit point in their Fourier spectrum.

Original languageEnglish
Pages (from-to)341-354
Number of pages14
JournalQuarterly of Applied Mathematics
Volume56
Issue number2
DOIs
StatePublished - 1 Jan 1998

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