Keynote – Nonlinear natural convection in porous media and the collapse of the wave function

A short review of the problem of nonlinear natural convection in a fluid saturated porous layer heated from below is presented. When the conditions for the onset of convection are met a wave function is obtained as the solution of the linearized equations expressed in terms of a Fourier expansion. Only one mode of this expansion survives at the onset of convection, a result that can be seen as the Collapse of the Wave function in a very similar fashion as in quantum mechanics, although the explanations of the latter are very distinct from the ones in quantum mechanics. The reasons behind the Collapse of the Wave function result in natural convection are discussed and the analysis is extended into the nonlinear domain of convection, by using a weak nonlinear analysis