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Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

Published online by Cambridge University Press:  27 November 2014

P. Deepu ,
Sameer Dawande  and
Saptarshi Basu
P. Deepu
Affiliation:
Indian Institute of Science, Bangalore 560012, India
Sameer Dawande
Affiliation:
Indian Institute of Science, Bangalore 560012, India
Saptarshi Basu*
Affiliation:
Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, linear stability analysis on a Newtonian fluid film flowing under the effect of gravity over an inclined porous medium saturated with the same fluid in isothermal condition is carried out. The focus is placed on the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on the shear mode and surface mode instabilities. The fluid–porous system is modelled by a coupled two-dimensional Navier–Stokes/Darcy problem. The perturbation equations are solved numerically using the Chebyshev collocation method. Detailed stability characteristics as a function of the depth ratio (the ratio of the depth of the fluid layer to that of the porous layer), the anisotropic parameter (the ratio of the permeability in the direction of the basic flow to that in the direction transverse to the basic flow) and the inhomogeneity functions are presented.

JFM classification

Instability: Absolute/convective instability Low-Reynolds-number flows: Porous media
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 762 , 10 January 2015 , R2
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Copyright
© 2014 Cambridge University Press 

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