Abstract
We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For Kibel numbers \(\cal{O}\)A A(1), the acoustic filtration law resembles a Darcy’s law, but with a conductivity which depends on the wave frequency and on the angular velocity. The bulk momentum balance shows new inertial terms which account for the convective and Coriolis accelerations. Three dispersive waves are pointed out. An investigation in the inertial flow regime shows that the two pseudo-dilatational waves have a cut-off frequency.
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J.-L. Auriault (1980) ArticleTitleDynamic behaviour of a porous medium saturated by a newtonian fluid Int. J. Eng. Sci. 18 775–785
J.-L. Auriault (1991) ArticleTitleHeterogeneous medium. Is an equivalent macroscopic description possible? Int. J. Eng. Sci. 29 IssueID7 785–795
Auriault, J.-L.: 1997, Poro-elastic media, in: U. Hornung (ed.), Homogenization and Porous Media, Interdisciplinary Applied mathematics, Vol. 6, Springer, New York, pp. 163–182
J.-L. Auriault (2004) ArticleTitleBody wave wave propagation in rotating elastic media Mech. Res. Commun. 31 21–27
J.-L. Auriault L. Borne R. Chambon (1985) ArticleTitleDynamics of porous saturated media, checking of the generalized law of Darcy J. Acoust. Soc. Am. 77 IssueID5 1641–1650
J.-L. Auriault C. Geindreau P. Royer (2000) ArticleTitleFiltration law in rotating porous media C.R.A.S. II b 328 779–784
J.-L. Auriault C. Geindreau P. Royer (2002) ArticleTitleCoriolis effects on filtration law in rotating porous media TIPM 48 315–330
A. Bensoussan J.-L. Lions G. Papanicolaou (1978) Asymptotic Analysis for Periodic Structures North Holland Amsterdam
M.A. Biot (1956a) ArticleTitleTheory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range J. Acoust. Soc. Am. 28 IssueID2 168–178
M.A. Biot (1956b) ArticleTitleTheory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range J. Acoust. Soc. Am. 28 IssueID2 179–191
M.A. Biot (1962) ArticleTitleMechanics of deformation and acoustic propagation in porous media J. Appl. Phys. 33 IssueID4 1482–1498
R. Burridge J.B. Keller (1981) ArticleTitlePoroelasticity equations derived from microstructure J.A.S.A. 70 IssueID4 1140–1146
C. Geindreau E. Sawicki J.-L. Auriault P. Royer (2004) ArticleTitleAbout Darcy’s law in non-Galilean frame Int. J. Numer. Anal. Meth. Geomech. 28 2295–3249
T. Levy (1979) ArticleTitlePropagation of waves in a fluid saturated porous elastic solid Int. J. Eng. Sci. 17 1005–1014
Sanchez-Palencia, E. 1980, Non Homogeneous Media and Vibration Theory, Vol. 127, Springer, New York. Lecture notes in Physics
P. Vadasz (1993) ArticleTitleFluid flow through heterogeneous porous media, in: a rotating square channel Transport Porous Media 12 43–54
P. Vadasz (1997) Flow in rotating porous media Plessis Prieur du (Eds) Fluid Transport in Porous Media Computational Mechanics Publications Southampton
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AURIAULT, JL. Acoustics of Rotating Deformable Saturated Porous Media. Transp Porous Med 61, 235–237 (2005). https://doi.org/10.1007/s11242-004-8214-x
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DOI: https://doi.org/10.1007/s11242-004-8214-x