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Steady streaming in a channel with permeable walls

Published online by Cambridge University Press:  28 August 2013

KONSTANTIN ILIN
KONSTANTIN ILIN*
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK email: [email protected]
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Abstract

We study steady streaming in a channel between two parallel permeable walls induced by oscillating (in time) injection/suction of a viscous fluid at the walls. We obtain an asymptotic expansion of the solution of the Navier–Stokes equations in the limit when the amplitude of normal displacements of fluid particles near the walls is much smaller than both the width of the channel and the thickness of the Stokes layer. It is shown that the steady part of the flow in this problem is much stronger than the steady flow produced by vibrations of impermeable boundaries. Another interesting feature of this problem is that the direction of the steady flow is opposite to what one would expect if the flow was produced by vibrations of impermeable walls.

Keywords

Boundary-layer theorySteady streamingAsymptotic methodsOscillating viscous flowsNavier-Stokes equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 1 , February 2014 , pp. 65 - 82
Copyright
Copyright © Cambridge University Press 2013 

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