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MARGINAL STABILITY ANALYSIS FOR A CONVECTIVE FLOW IN A POROUS MEDIUM WITH VERTICALLY VARYING RESISTIVITY

Том 23, Выпуск 1, 2020, pp. 69-79
DOI: 10.1615/JPorMedia.2019026768
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Краткое описание

We consider a convective flow in a horizontal porous medium to investigate the marginal stability due to linear variation in resistivity in the vertical direction. The flow in the porous medium can be described by a system of partial differential equations consisting of the continuity equation for conservation of mass, the heat equation for conservation of energy, and the momentum-Darcy equation for conservation of momentum. The resistivity of the medium is defined as the ratio of dynamic viscosity to permeability. Assuming a vertically varying basic state, we apply a linear stability approach to compute the critical Rayleigh and wave numbers from the linear system. Marginal stability curves and linear solutions are obtained numerically using fourth-order Runge-Kutta and shooting methods for different values of the resistivity parameter. This work is important for applications as in the case of a porous layer of underground water whose permeability varies vertically.

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