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Home » Issues » Archive of Issues » 2015 - 1 issue » pp. 107-116

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Russia Perm
Year
2015
Volume
25
Issue
1
Pages
107-116
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Section Mechanics
Title Stability of the flow over saturated porous medium containing dissolved admixture
Author(-s) Tsiberkin K.B.a
Affiliations Perm State National Research Universitya
Abstract 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, admixture transport, Brinkman model
UDC 532.5.013.4
MSC 76E05, 76S05
DOI 10.20537/vm150112
Received 8 February 2015
Language Russian
Citation Tsiberkin K.B. Stability of the flow over saturated porous medium containing dissolved admixture, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 107-116.
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