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Evolution of a long-wave train in loss of stability of a phase interface in geothermal systems. (English. Russian original) Zbl 1210.76078
Fluid Dyn. 43, No. 1, 97-104 (2008); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2008, No. 1, 110-119 (2008).
Summary: The transition to instability of phase interfaces in geothermal systems when a water stratum overlies a steam stratum and the most unstable mode corresponds to zero wavenumber is considered.
The nonlinear Kolmogorov-Petrovskii-Piskunov equation describing the evolution of a narrow strip of weakly unstable modes is obtained. This equation is an analog of the well-known Ginzburg-Landau equation corresponding to the case of destabilization of modes with finite wavenumbers. It is shown that in the neighborhood of the critical points there exist two locations of the plane phase interface which coincide at the instant at which the instability threshold is reached and then disappear.

MSC:
76E17 Interfacial stability and instability in hydrodynamic stability
76E20 Stability and instability of geophysical and astrophysical flows
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