Geodesic
Stability of the flow over saturated porous medium containing dissolved admixture
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 1, pp. 107-116

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A two-layer system consisting of a porous layer of finite thickness and a uniform fluid layer on top is considered. A rigid wall bounds the porous layer from below, while the upper fluid surface is assumed to be undeformable. We study the process of admixture extraction from the porous layer and its influence on the stability of the stationary plane-parallel flow above it. We describe a porous layer using a Brinkman model with interface boundary conditions by Ochoa–Tapia–Whitaker. We obtain an exact and an approximate solution for the concentration profile. The quasistationary velocity profile is obtained using “frozen” concentration distribution. We solve a linear stability problem for the plane-parallel stationary flow in a wide range of system parameters. Oscillatory instability evolved in the system at the sufficient flow velocity corresponds to traveling waves near the interface. We show that the convective and diffusion transport practically does not affect the structure of neutral stability curves and Reynolds numbers.
Keywords: flow over porous medium, two-layer system, bimodality, flow instability, Brinkman model.
Mots-clés : admixture transport 
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     author = {K. B. Tsiberkin},
     title = {Stability of the flow over saturated porous medium containing dissolved admixture},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {107--116},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2015_25_1_a11/}
}
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K. B. Tsiberkin. Stability of the flow over saturated porous medium containing dissolved admixture. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 1, pp. 107-116. http://geodesic.mathdoc.fr/item/VUU_2015_25_1_a11/