Summary
Bénard-Marangoni instabilities are theoretically discussed: emphasis is placed on the role of negative Rayleigh and Marangoni numbers. Marginal, supercritical and subcritical instabilities are respectively examined.
The first part is concerned with the response of an unbounded fluid layer with respect to small disturbances. A variational principle describing marginal stability is proposed. Rayleigh-Ritz method is used to obtain approximate solutions for the critical Rayleigh and Marangoni numbers. In a second part, corrections to the linear theory, by including weak nonlinearities, are introduced. The amplitude of the supercritical temperature and velocity fields are calculated in the framework of Stuart's shape approximation. Finally, the possibility of subcritical instability with respect to disturbances of arbitrary amplitude is investigated by the method of energy.
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Lebon, G., Cloot, A. Buoyancy and surface-tension driven instabilities in presence of negative Rayleigh and Marangoni numbers. Acta Mechanica 43, 141–158 (1982). https://doi.org/10.1007/BF01176278
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DOI: https://doi.org/10.1007/BF01176278