Technical Papers
Nov 19, 2012

Laboratory Measurement of Seabed Shear Stress and the Slip Factor over a Porous Seabed

Publication: Journal of Engineering Mechanics
Volume 139, Issue 10

Abstract

This paper provides a simple relationship to theoretically estimate the wave friction factor in various flow regimes in porous media based on the slip factor formula. The theoretical formula shows that the wave friction factor varies inversely with the relative bed roughness, A/ks, over a rough bed and that it can be conveniently determined if wave conditions and sediment parameters are known without using a specific regression formula deduced from experiments. A laboratory experiment that directly measures the wave-driven bed shear stress dominant in the turbulent regime with a permeable bed is used to examine the newly derived relationship. In the laminar regime, the comparison demonstrates that the theoretical results determined by the proposed formula are in good agreement with existing measurements. In the turbulent-rough regime, the influence of eddy viscosity is considered in the slip factor formula and the zero-equation model is used in estimating the average eddy viscosity. The theoretical wave friction factor is reasonably close to the experimental measurement, and considerably better than that obtained by other existing regressions. It is also found that the wave friction factor in the small A/ks zone can be described by the present model, with comparisons showing that the slip factor theory can be extended to estimate the wave friction factor in the turbulent-rough regime. Additionally, the proposed relationship is demonstrated to be effectively used in an alternate rough bed. Experimental results further indicate that the wave friction factor in a porous medium is affected by the permeability of the sediment.

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Acknowledgments

This paper was completed with grants from the National Science Council–International Wave Dynamics Research Center (NSC 102-2911-I-006-302). The authors thank the reviewers for providing comments.

References

Bagnold, R. A. (1946). “Motion of waves in shallow water interaction between waves and sand bottom.” Proc. R. Soc. London, Ser. A Math. Phys. Sci., 187(1008), 1–48.
Barnes, M. P., O’Donoghue, T., Alsina, J. M., and Baldock, T. E. (2009). “Direct bed shear stress measurements in bore-driven swash.” Coastal Eng., 56(8), 853–867.
Bear, J. (1972). Dynamics of fluids in porous media, Elsevier, New York.
Beavers, G. S., and Joseph, D. D. (1967). “Boundary conditions at a naturally permeable wall.” J. Fluid Mech., 30(1), 197–207.
Blevins, R. D. (1977). Flow-induced vibration, Van Nostrand Reinhold, New York.
Boussinesq, J. (1877). Essai sur la theorie des eaux courantes, Imprimerie Nationale, Paris (in French).
Chen, Y. Y., Chen, G. Y., and Lin, C. H. (2012). “The slip factor and slip velocity on a permeable bed.” J. Coastal Res., 28(2), 360–368.
Chen, Y. Y., Chen, G. Y., Lin, C. H., and Chou, C. L. (2010). “Progressive waves in real fluids over a rigid permeable bottom.” Coast. Eng. J., 52(1), 17–42.
Chu, Y. H., and Gelhar, L. W. (1972). “Turbulent pipe flow with granular Permeable boundaries.” Rep. No. 148, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA.
Davies, A. G. (1986). “A model of oscillatory rough turbulent boundary layer.” Estuarine Coastal Shelf Sci., 23(3), 353–374.
Ding, L., and Zhang, Q. H. (2010). “Lattice Boltzmann simulation to characterize roughness effects of oscillatory boundary layer flow over a rough bed.” Proc., 32nd Int. Conf. on Coastal Engineering, Coastal Engineering Research Council, Reston, VA.
Dixen, M., Hatipoglu, F., Sumer, B. M., and Fredsøe, J. (2008). “Wave boundary layer over a stone-covered bed.” Coastal Eng., 55(1), 1–20.
Fredsøe, J., and Deigaard, R. (1992). Mechanics of coastal sediment transport, World Scientific, Singapore.
Grass, A. J., Simons, R. R., Maciver, R. D., Mansour, M. T., and Kalopedis, A. (1995). “Shear cell for direct measurement of fluctuating bed shear stress vector in combined wave/current flow.” Proc., 26th IAHR Congress (HYDRA 2000), Vol. 1, Thomas Telford, London, 415–420.
Gualtieri, C. (2010). “Numerical simulation of transition layer at a fluid- porous interface.” Proc., 15th Int. Congress on Environmental Modelling and Software Modelling for the Environment’s Sake, International Environmental Modelling and Software Society (iEMSs), Guelph, ON, Canada.
Hsieh, P.-c., Dai, H.-h., and Huang, L.-h. (2003). “Laminar water wave and current passing over porous bed.” J. Eng. Mech., 129(6), 655–664.
Hsu, T. W., and Ou, S. H. (1997). “Wave boundary layers in rough turbulent flow.” Ocean Eng., 24(1), 25–43.
Huo, G., Wang, Y. G., Yin, B. S., and You, Z. J. (2007). “A new measure for direct measurement of the bed shear stress of wave boundary layer in wave flume.” J. Hydrodynam, 19(4), 517–524.
Jensen, B. L., Sumer, B. M., and Fredsøe, J. (1989). “Turbulent oscillatory boundary layers at high Reynolds numbers.” J. Fluid Mech., 206, 265–297.
Jonsson, I. G. (1966). “Wave boundary layer and friction factors.” Proc., 10th Coastal Engineering Conf., Vol. I, Coastal Engineering Research Council, Reston, VA, 127–148.
Jonsson, I. G. (1980). “A new approach to oscillatory rough turbulent boundary layers.” Ocean Eng., 7(1), 109–152.
Jonsson, I. G., and Carlsen, N. A. (1976). “Experimental and theoretical Investigations in an oscillatory turbulent boundary layer.” J. Hydraul. Res., 14(1), 45–60.
Justesen, P. (1988). “Prediction of turbulent oscillatory flow over rough beds.” Coastal Eng., 12(3), 257–284.
Kajiura, K. (1968). “A model of the bottom boundary layer in water waves.” Bull. Earthquake Res. Inst., Univ. Tokyo, 46, 75–123.
Kamphuis, J. W. (1975). “Friction factor under oscillatory waves.” J. Wtrwy., Harb. and Coast. Engrg. Div., 101(2), 135–144.
Liu, Z. (2001). Sediment transport, Aalborg Univ., Aalborg, Denmark.
Lowe, R. J., Shavit, U., Falter, J. L., Koseff, J. R., and Monismith, S. G. (2008). “Modeling flow in coral communities with and without waves: A synthesis of porous media and canopy flow approaches.” Limnol. Oceanogr., 53(6), 2668–2680.
Mirfenderesk, H., and Young, I. R. (2003). “Direct measurement of the bottom friction factor beneath surface gravity waves.” Appl. Ocean Res., 25(5), 269–287.
Munoz-Goma, R. J., and Gelhar, L. W. (1968). “Turbulent pipe flow with rough and porous walls.” Rep. No. 109, Hydrodynamics Laboratory, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA.
Nield, D. A., and Bejan, A. (1992). Convection in porous media, Springer, New York.
Nielsen, P. (1992). Coastal bottom boundary layers and sediment transport, World Scientific, Singapore.
Nielsen, P., and Guard, P. A. (2010). “Vertical scales and shear stresses in wave boundary layers over movable beds.” Proc., 32nd Int. Conf. on Coastal Engineering, Coastal Engineering Research Council, Reston, VA.
Rankin, K. L., and Hires, R. I. (2000). “Laboratory measurement of bottom shear stress on a movable bed.” J. Geophys. Res., 105(C7), 17011–17019.
Riedel, P. H., and Kamphuis, J. W. (1973). “A shear plate for use in oscillatory flow.” J. Hydraul. Res., 11(2), 137–156.
Ruff, J. F., and Gelhar, L. W. (1970). “Porous boundary effects in turbulent shear flow.” Rep. No. 126, Water Resources and Hydrodynamics Laboratory, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA.
Saffman, P. G. (1971). “On the boundary condition at the surface of a porous medium.” Stud. Appl. Math., 50(2), 93–101.
Seelam, J. K., Guard, P. A., and Baldock, T. E. (2011). “Measurement and modeling of bed shear stress under solitary waves.” Coastal Eng., 58(9), 937–947.
Simons, R., Myrhaug, D., Thais, L., Chapalain, G., Holmedal, L.-E., and Maclver, R. (2000). “Bed friction in combined wave-current flows.” Proc., Coastal Engineering Conf., Vol. 1, ASCE, New York, 216–226.
Sleath, J. F. A. (1984). Sea bed mechanics, Wiley, New York.
Sleath, J. F. A. (1987). “Turbulent oscillatory flow over rough beds.” J. Fluid Mech., 182, 360–409.
Suga, K., and Nishiguchi, S. (2009). “Computation of turbulent flows over porous/fluid interfaces.” Fluid Dyn. Res., 41(1), 012401.
Vinogradova, O. I. (1995). “Drainage of a thin liquid film confined between hydrophobic surfaces.” Langmuir, 11(6), 2213–2220.
White, F. M. (1991). Viscous fluid flow, McGraw Hill, New York.
You, Z. J. (2000). “A simple model of sediment initiation under waves.” Coastal Eng., 41(4), 399–412.
You, Z. J., and Yin, B. S. (2007). “Direct measurement of bottom shear stress under water waves.” J. Coastal Res., SI50, 1132–1136.
You, Z. J., Wilkinson, D. L., and Nielsen, P. (1992). “Velocity distribution in a turbulent oscillatory boundary layer.” Coastal Eng., 18(1–2), 21–38.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 139Issue 10October 2013
Pages: 1372 - 1386

History

Received: May 8, 2012
Accepted: Nov 15, 2012
Published online: Nov 19, 2012
Published in print: Oct 1, 2013

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Authors

Affiliations

Jing-Hua Lin
Postdoctoral Fellow, International Wave Dynamic Research Center (IWDRC), National Cheng Kung Univ., No. 1, University Rd., Tainan City 701, Taiwan (R.O.C.).
Guan-Yu Chen
Associate Professor, Institute of Applied Marine Physics and Undersea Technology, National Sun Yat-Sen Univ., No. 70, Lianhai Rd., Gushan District, Kaohsiung City 804, Taiwan (R.O.C.).
Yang-Yih Chen [email protected]
Director, Tainan Hydraulics Laboratory, National Cheng Kung Univ., 5th F., No. 500, Sec. 3, Anming Rd., Annan District, Tainan City 70955, Taiwan (R.O.C.); and Professor, Dept. of Marine Environment and Engineering, National Sun Yat-Sen Univ., No. 70, Lianhai Rd., Gushan District, Kaohsiung City 804, Taiwan (R.O.C.) (corresponding author). E-mail: [email protected]

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