Criteria of hydrodynamic instability of a phase interface in hydrothermal systems

The loss of stability of a vertical phase flow in a geothermal system in which a liquid layer overlies a vapor layer is considered. The loss of stability criteria are obtained in explicit form. It is found that when the physical parameters of the system are varied the transition to phase interface instability can be realized by means of one of the following mechanisms: the transition occurs spontaneously for any perturbation wavenumber (degenerate case); an unstable wavenumber arises at infinity; the instability threshold is determined by a double zero wavenumber. In the latter case the transition to instability is accompanied by simple resonance bifurcation. As a result of this bifurcation, secondary regimes dependent on the horizontal coordinate branch off from the basic regime describing the horizontally-homogeneous vertical phase flows.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 100–109. Original Russian Text Copyright © 2004 by Ilichev and Tsypkin.