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The Quarterly Journal of Mechanics and Applied Mathematics 1995 48(1):57-75; doi:10.1093/qjmam/48.1.57
© 1995 by Oxford University Press
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TIME-GROWTH AND CORRELATION LENGTH OF FLUCTUATIONS IN THERMOCAPILLARY CONVECTION WITH SURFACE DEFORMATION

V. C. REGNIER and G. LEBON

( Institut de Physique B5, Université de Liège Sart Tilman B-4000 Liège, Belgium )

Thermocapillary instabilities with surface deformation in a fluid layer heated from below are studied; both gravity and capillary waves are considered. The aim of the present work is to determine the dependence of the time growth of fluctuations and their correlation length in supercritical conditions with respect to the crispation, Bond, Prandtl and Biot numbers. Two kinds of instabilities are analysed: the ‘classical’ Marangoni mode corresponding to wave-number approximately equal to two and the long-wave mode for which the wave-number is zero.


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