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Growth of fluctuations near the Bénard-Marangoni convective instability. (English) Zbl 0532.76047

The effects of surface tension gradients on the behaviour of velocity and temperature fluctuations near the onset of convective instability are considered. A horizontal fluid layer bounded below by a flat plate and above by a free surface is discussed. The Rayleigh-Bénard and the Bénard-Marangoni instabilities are studied and the growth rates calculated in terms of the various dimensionless numbers of the problem. The close analogy of the results with the Landau theory of phase transitions is pointed out. Many results, related to the relaxation times and the growth rates, are obtained in a simple way using the analogy.
Reviewer: E.S.R.Gopal

MSC:

76E15 Absolute and convective instability and stability in hydrodynamic stability
76E20 Stability and instability of geophysical and astrophysical flows
82B26 Phase transitions (general) in equilibrium statistical mechanics
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