Andrey Il’ichev Steklov Mathematical Institute, Moscow George Tsypkin

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Presentation transcript:

Weakly-nonlinear regimes near the threshold of instability in geothermal systems Andrey Il’ichev Steklov Mathematical Institute, Moscow George Tsypkin Institute for problems in mechanics, Moscow

Geothermal systems Geometry of the problem; is a high-permeability domain, 1 is a low-permeability domain occupied by water, 2 is the low-permeability domain occupied by vapor, is the high-permeability domain. .

Equations and boundary conditions div =0, , , div =0, , , , , , , , Log , ,

Vertical flows

Linear stability

Long-wave instability

KPP equation