naa a22 4500 510812376 CHVBK 20180411083448.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1134/S0081543813040159 doi (NATIONALLICENCE)springer-10.1134/S0081543813040159 Classification of the types of instability of vertical flows in geothermal systems [Elektronische Daten] [A. Il'ichev, G. Tsypkin] 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. Pleiades Publishing, Ltd., 2013 Il'ichev A. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut Tsypkin G. Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, korp. 1, 119526, Moscow, Russia aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 179-188 0081-5438 281:1<179 2013 281 11501 https://doi.org/10.1134/S0081543813040159 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813040159 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Il'ichev A. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut NATIONALLICENCE 700 1- Tsypkin G. Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, korp. 1, 119526, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 179-188 0081-5438 281:1<179 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer