Geodesic
Classification of the types of instability of vertical flows in geothermal systems
Informatics and Automation, Modern problems of mechanics, Tome 281 (2013), pp. 188-198

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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. 
@article{TRSPY_2013_281_a14,
     author = {A. T. Il'ichev and G. G. Tsypkin},
     title = {Classification of the types of instability of vertical flows in geothermal systems},
     journal = {Informatics and Automation},
     pages = {188--198},
     publisher = {mathdoc},
     volume = {281},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_281_a14/}
}
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A. T. Il'ichev; G. G. Tsypkin. Classification of the types of instability of vertical flows in geothermal systems. Informatics and Automation, Modern problems of mechanics, Tome 281 (2013), pp. 188-198. http://geodesic.mathdoc.fr/item/TRSPY_2013_281_a14/