Tr. Mat. Inst. Steklova, 2013, Volume 281, Pages 188–198
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
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.
|Russian Foundation for Basic Research
|The work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00335a and 11-01-12051-ofi-m-2011).
PDF file (206 kB)
Proceedings of the Steklov Institute of Mathematics, 2013, 281, 179–188
Received in September 2012
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, 188–198; Proc. Steklov Inst. Math., 281 (2013), 179–188
Citation in format AMSBIB
\by A.~T.~Il'ichev, G.~G.~Tsypkin
\paper Classification of the types of instability of vertical flows in geothermal systems
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\publ MAIK Nauka/Interperiodica
\jour Proc. Steklov Inst. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|