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Wave-induced boundary layer flows above and in a permeable bed

Published online by Cambridge University Press:  26 April 2006

Philip L.-F. Liu ,
Matthew H. Davis  and
Sean Downing
Philip L.-F. Liu
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
Matthew H. Davis
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
Sean Downing
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

In this paper, the oscillatory and steady streaming velocities over a permeable bed are studied both theoretically and experimentally. Three different sizes of glass beads are used to construct permeable beds in laboratory experiments: the diameters of the glass beads are 0.5 mm, 1.5 mm, and 3.0 mm, respectively. Several experiments are performed using different wave parameters. A one-component laser-doppler velocimeter (LDV) is used to measure the horizontal velocity component inside the Stokes boundary layer above the solid and permeable surfaces. It is observed that neither oscillatory nor steady velocity components vanish on the permeable surface. The ‘slip velocities’ increase with increasing permeability. Based on the laminar flow assumption and the order of magnitude of the parameters used in the experiments, a perturbation theory is developed for the oscillatory velocity and the steady wave-induced streaming in the boundary layers above and inside the permeable bed. The theory confirms many experimental observations. The theory also provides the damping rate and the phase changes caused by the permeable bed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 195 - 218
Copyright
© 1996 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Batchelor, G. K. 1974 Transport properties of two-phase materials with random structure. Ann. Rev. Fluid Mech 6, 227–255.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Meck. 30, 197–207.Google Scholar
Beech, N. W. 1978 Laser Doppler measurements in the oscillatory boundary layer beneath water waves. DSIA Elektronik No. 23, September.Google Scholar
Brinkman, H. C. 1947 On the permeability of media consisting of closely packed porous particles. Appl. Sci. Res. Al, 81–86.Google Scholar
Carter, T. G., Liu, P. L.-F. & Mei, C. C. 1973 Mass transport by waves and offshore sand bedforms. J. Waterways, Harbor, Coastal Engineering Div., ASCE 99, 165–184.Google Scholar
Dagan, G. 1979 The generalization of Darcy's law for nonuniform flows. Water Resources Res. 15, 1–7.Google Scholar
Davis, M. H. 1995 Water wave-induced streaming in the bottom boundary layer over a permeable bed. MS thesis, School of Civil and Environmental Engineering, Cornell University.
Downing, S. L. 1993 Measurements of the velocity structure in the bottom boundary layer under ocean waves. MS thesis, Department of Physics, Cornell University.
Happel, J. & Brenner, H. 1985 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Howells, I. D. 1974 Drag due to the motion of Newtonian fluid through a sparse random array of small fixed rigid objects. J. Fluid Mech. 64, 449–475.Google Scholar
Hwung, H. H. & Lin, C. 1990 The mass transport of wave propagating on a sloppiing bottom. 22nd Conf. Coastal Engng, pp. 544–556.Google Scholar
Liu, P. L.-F. 1973 Damping of water waves over a porous bed. J. Hydraulic Engng, ASCE 99, 2263–2271.Google Scholar
Liu, P. L.-F. 1977 Mass transport in water waves propagated over a permeable bed. Coastal Engng 1, 79–96.Google Scholar
Liu, P. L.-F. & Dalrymple, R. A. 1984 The damping of gravity waves due to percolation. Coastal Engng 8, 33–49.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535–581.Google Scholar
Lundgren, T. S. 1972 Slow flow through stationary random beds and suspensions of spheres. J. Fluid Mech. 51, 273–299.Google Scholar
Putnam, J. A. 1949 Loss of water wave energy due to percolation in a permeable sea bottom. Trans. Am. Geophys. Union 30, 349–356.Google Scholar
Reid, R. O. & Kajiura, K. 1957 On the damping of gravity waves over a permeable sea bed. Trans. Am. Geophys. Union 38, 362–666.Google Scholar
Russell, R. C. H. & Osorio, J. D. C. 1957 An experiment investigation of drift profiles in a closed channel. Proc. 6th Conf. Coastal Engng, ASCE, pp. 171–193.Google Scholar
Skjelbreia, J. E. 1987 Observations of breaking waves on slopping bottoms by use of laser doppler velocimetry. W. M. Keck Laboratory of Hydraulics and Water Resources, Caltech., Rep. KH-R-48.Google Scholar
Sleath, J. F. A. 1972 A second approximation to mass transport by water waves. J. Marine Res. 30, 295–304.Google Scholar
Sleath, J. F. A. 1978 Discussion of “Mass transport in water waves propagated over a permeable bed” (by P.L.-F. Liu). Coastal Engng 2, 169–171.Google Scholar
Sleath, J. F. A. 1984 Measurements of mass transport over a rough bed. 19th Conf. Coastal Engng, pp. 1149–1160.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455.Google Scholar
Tam, C. K. W. 1969 The drag on a cloud of spherical particles in low Reynolds number flow. J. Fluid Mech. 38, 537–546.Google Scholar