Abstract
A general local potential is written for the study of the stability of parallel flows with an imposed temperature gradient (normal or ‘adverse’). This local potential has two well defined limits: the Bénard problem for a Reynolds number equal to zero, and the Orr-Sommerfeld problem for a vanishing Rayleigh number. The variational technique introduced by Prigogine and Glansdorff, leads us formally to a characteristic equation, from which it is possible to deduce the influence of a laminar flow on the Bénard instability: the critical Rayleigh number increases with the Reynolds number. On the other hand, heating a fluid from above seems to delay turbulence.
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