On the Principle of Exchange of Stabilities in Rayleigh-Bénard Convection, II - No-slip Boundary Conditions
نویسنده
چکیده
Rayleigh-Bénard convection with internal heat sources and a variable gravity field is treated with no-slip boundary conditions. It is proved that the principle of exchange of stabilities holds at all Prandtl numbers, as long as the gravity field and the integral of the heat sources both have the same sign. The proof is based on the idea of a positive operator, and uses the positivity properties of Green’s function. The generalized Green’s function is also employed.
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