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Long-wave-induced flows in an unsaturated permeable seabed

Published online by Cambridge University Press:  14 August 2007

PHILIP L.-F. LIU ,
YONG SUNG PARK  and
JAVIER L. LARA
PHILIP L.-F. LIU
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
YONG SUNG PARK
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
JAVIER L. LARA
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

We present both analytical and numerical solutions describing seepage flows in an unsaturated permeable seabed induced by transient long waves. The effects of compressibility of pore water in the seabed due to a small degree of unsaturation are considered in the investigation. To make the problem tractable analytically, we first focus our attention on situations where the horizontal scale of the seepage flow is much larger than the vertical scale. With this simplification the pore-water pressure in the soil column is governed by a one-dimensional diffusion equation with a specified pressure at the water–seabed interface and the no-flux condition at the bottom of the seabed. Analytical solutions for pore-water pressure and velocity are obtained for arbitrary transient waves. Special cases are studied for periodic waves, cnoidal waves, solitary waves and bores. Numerical solutions are also obtained by simultaneously solving the Navier–Stokes equations for water wave motions and the exact two-dimensional diffusion equation for seepage flows in the seabed. The analytical solutions are used to check the accuracy of the numerical methods. On the other hand, numerical solutions extend the applicability of the analytical solutions. The liquefaction potential in a permeable bed as well as the energy dissipation under various wave conditions are then discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007 , pp. 323 - 345
Copyright
Copyright © Cambridge University Press 2007

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References

Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Chorin, A. J. 1968 Numerical solution of the Navier-Stokes equations. Math. Comput. 22, 745–762.CrossRefGoogle Scholar
Dalrymple, R. A. & Liu, P. L.-F. 1978 Waves over soft muds: a two-layer fluid model. J. Phys. Oceanogr. 8, 1121–1131.2.0.CO;2>CrossRefGoogle Scholar
Goring, D. K. 1978 Tsunamis – the propagation of long waves onto a shelf. Rep. KH-R-9. W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology.Google Scholar
Jeng, D. S. 2003 Wave-induced sea floor dynamics. Appl. Mech. Rev. 56, 407–429.CrossRefGoogle Scholar
Lin, P. 1998 Numerical modeling of breaking waves. PhD Thesis, Cornell University.Google Scholar
Lin, P. & Liu, P. L.-F. 1998 A numerical study of breaking waves in the surf zone J. Fluid Mech. 359, 239–264.CrossRefGoogle Scholar
Liu, P. L.-F. 1973 Damping of water waves over porous bed. J. Hydraul. Div. ASCE 99, 2263–2271.CrossRefGoogle Scholar
Liu, P. L.-F. & Chan, I.-C. 2007 a A note on the effects of a thin visco-elastic mud layer on small amplitude water wave propagation Coastal Engng 54, 233–247.CrossRefGoogle Scholar
Liu, P. L.-F. & Chan, I.-C. 2007 b On long wave propagation over a fluid-mud seabed J. Fluid Mech. 579, 467–480.CrossRefGoogle Scholar
Liu, P. L.-F. & Orfila, A. 2004 Viscous effects on transient long wave propagation. J. Fluid Mech. 520, 83–92.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1974 On the mass, momentum, energy and circulation of a solitary wave Proc. R. Soc. Lond. A 337, 1–13.Google Scholar
Macpherson, H. 1980 The attenuation of water waves over a non-rigid bed. J. Fluid Mech. 97, 721–742.CrossRefGoogle Scholar
Madsen, O. S. 1974 Stability of a sand bed under breaking waves. In Proc. 14th Conf. Coastal Engng, vol. 2, pp. 776–794.Google Scholar
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. John Wiley & Sons.Google Scholar
Mei, C. C. & Liu, P. L.-F. 1993 Surface waves and coastal dynamics. Annu. Rev. Fluid Mech. 25, 215–240.CrossRefGoogle Scholar
Miles, J. W. 1979 On the Korteweg-de Vries equation for a gradually varying channel. J. Fluid Mech. 91, 181–190.CrossRefGoogle Scholar
Moshagen, H. & Torum, A. 1975 Wave induced pressures in permeable seabeds. J. Waterways, Harbor, and Coastal Engng. Div. ASCE, 49–57.Google Scholar
Oumeraci, H. & Kudella, M. 2004 Large scale experiments on a caisson breakwater. Tech. Rep. Technical Univ. of Braunschweig, Leichtweiss-Institute.Google Scholar
Packwood, A. R. & Peregrine, D. H. 1980 The propagation of solitary waves and bores over a porous bed. Coastal Engng 3, 221–242.CrossRefGoogle Scholar
Sumer, B. M. & Fredsoe, J. 2002 The Mechanics of Scour in the Marine Environment. World Scientific.CrossRefGoogle Scholar
Wen, J. & Liu, P. L.-F. 1998 Effects of seafloor conditions on water wave damping. In Advances in Fluid Mechanics: Free Surface Flows and Viscosity (ed. Tyrand, P. A.), vol. 16, pp. 145–178.Google Scholar
Yamamoto, T., Koning, H. L., Sellmeijer, H. & van Hijum, E. 1978 On the response of a poro-elastic bed to water waves. J. Fluid Mech. 87, 193–206.CrossRefGoogle Scholar