Minimum rate of entropy production variational formulation and preferred mode of motion in thermal instability

This paper recasts the complete variational formulation of the linear thermal instability as a particular case of the thermodynamic principle of minimum rate of entropy production. This principle causes the various solutions which correspond to the same Rayleigh Number to become distinguishable, and prefers one of them. The treated examples are the infinite horizontal layer; the finite horizontal layer; the supercritical Rayleigh Number case; the determination of the flow direction. The hypothesis of maximum heat flux is shown to be derivable from this principle. Finally the principle is shown to be representable by the Knops-Wilkes functional, and to result from the Movchan-Liapunov general theorems on stability, i.e. to also have a purely mathematical basis.