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Classification of the types of instability of vertical flows in geothermal systems A. T. Il'icheva, G. G. Tsypkinb a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia b Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia Abstract: Stability of vertical flows in geothermal systems is investigated in the case when the domain occupied by water (heavy fluid) is located over the domain occupied by vapor. It is found that under the transition to an unstable regime in a neighborhood of the existing solution, a pair of new solutions appears as a result of the turning point bifurcation. We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of the plane surface of the water-to-vapor phase transition. It is shown that such perturbations obey the generalized Ginzburg–Landau–Kolmogorov–Petrovsky–Piscounov equation.
DOI: https://doi.org/10.1134/S0371968513020155   Full text:
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English version: Proceedings of the Steklov Institute of Mathematics, 2013, 281, Bibliographic databases:    Document Type: Article UDC: 532.546 Received in September 2012 Citation: A. T. Il'ichev, G. G. Tsypkin, “Classification of the types of instability of vertical flows in geothermal systems”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 
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