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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2020, Volume 30, Issue 1, Pages 134–144 (Mi vuu715)  

MECHANICS

On the porosity influence on stability of flow over porous medium

K. B. Tsiberkin

Perm State National Research University, ul. Bukireva, 15, Perm, 614990, Russia

Abstract: The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than $0.7$, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin–Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

Keywords: porous medium, interface, flow stability.

Funding Agency Grant Number
Russian Science Foundation 18-71-00057
The study was funded by the Russian Science Foundation, project 18-71-00057.


DOI: https://doi.org/10.35634/vm200110

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Bibliographic databases:

UDC: 532.526, 536.25
MSC: 76E17, 76S05
Received: 10.01.2020

Citation: K. B. Tsiberkin, “On the porosity influence on stability of flow over porous medium”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:1 (2020), 134–144

Citation in format AMSBIB
\Bibitem{Tsi20}
\by K.~B.~Tsiberkin
\paper On the porosity influence on stability of flow over porous medium
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 1
\pages 134--144
\mathnet{http://mi.mathnet.ru/vuu715}
\crossref{https://doi.org/10.35634/vm200110}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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