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Engineering Journal: Science and Innovation, 2013, Issue 2, Pages 44–13 (Mi engj1)  

Interaction of stabilizing and destabilizing factors and bifurcations of phase transition fronts

A. T. Ilicheva, G. G. Tsypkinb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

Abstract: We study the competition between the Rayleigh–Taylor instability and stabilization by the vertical flow through the boundary ofphase transition in geothermal systems in dependence on the thickness of the low-permeability layer and permeability for fixed pressure drop and homogeneous conditions at the instant borders of the low-permeability layer. This competition becomes apparent by non-uniqueness of localization ofplane phase transition fronts, at least one of which being always unstable. The multiple fronts appear as a result of bifurcation from the unique stable front. In a neighborhood of the bifurcation point dynamics of a narrow band of weakly unstable and weakly nonlinear modes is described by one form of the nonlinear Kolmogorov–Petrovsky–Piscounov equation (KPP).

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-12051-офи-м
11-01-00335


DOI: https://doi.org/10.18698/2308-6033-2013-2-608


Document Type: Article

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