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Catastrophic transition to instability of evaporation front in a porous medium. (English) Zbl 1151.76480
Summary: Instability of a water layer located over an air-vapor layer in a horizontally infinite two dimensional domains of a porous medium is considered. A new mechanism of transition to instability of vertical flows developed in such a system is treated when the most unstable normal mode is affiliated with the zero wave number. Secondary structures bifurcating from the vertical base flow in a neighborhood of the threshold of instability obey the Kolmogorov-Petrovsky-Piscounov (KPP) diffusion-type equation. For the transition in question the KPP equation represents the analogue of the Ginzburg-Landau equation for the transition when the most unstable mode has a nonzero wave number. It is shown that in some neighborhood of the critical parameters there exist two different plane phase transition interfaces coinciding at the threshold of instability and ceasing to exist when the threshold is overcome. One of these interfaces is unstable, whereas the other is stable. It is shown nevertheless, that even the stable interface is destroyed by some perturbations of the unstable one due to nonlinear interplay of disturbances.

MSC:
76E17 Interfacial stability and instability in hydrodynamic stability
76T10 Liquid-gas two-phase flows, bubbly flows
76S05 Flows in porous media; filtration; seepage
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