Propagation of Water Waves over Rigid Rippled Beds
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 128, Issue 5
Abstract
A numerical scheme was developed to solve the unsteady, two-dimensional Navier-Stokes equations and the exact free-surface boundary conditions for simulating the propagation of water waves over rigid rippled beds. A boundary-fitted coordinate system was used in this model. The accuracy of the numerical scheme was verified by comparing the numerical results for the velocity fields on the rippled bed with the experimental data. For the periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. To provide information for understanding the possible mechanism of sediment transport around the rippled bed, trajectories of the fluid particles with initial locations close to the ripples were determined. One of our main results showed that as a solitary wave passes over rigid ripples, the fluid particles near the bed are lifted by the primary vortices induced at the lee side of the ripple crest and are transported in the opposite direction from the wave. This is different from what occurs in the case of periodic waves, where the fluid particles are transported in the direction of the waves.
Get full access to this article
View all available purchase options and get full access to this article.
References
Blondeaux, P.(1990). “Sand ripples under sea waves. Part 1: Ripple formation.” J. Fluid Mech., 218, 1–17.
Blondeaux, P., Foti, E., and Vittori, G.(2000). “Migrating sea ripples.” Eur. J. Mech. B-Fluids, 19, 285–301.
Blondeaux, P., and Vittori, G.(1991). “Vorticity dynamics in an oscillatory flow over a rippled bed.” J. Fluid Mech., 226, 257–289.
Blondeaux, P., and Vittori, G. (1999). “Boundary layer and sediment dynamics under sea waves.” Advances in coastal and ocean engineering, P. L. F. Liu, ed., Vol. 4, World Scientific, Singapore, 133–190.
Chan, R. K. C., and Street, R. L.(1970). “A computer study of finite-amplitude water waves.” J. Comput. Phys., 6(1), 68–94.
Chen, C. J., and Chen, H. C. (1982). “The finite-analytic method.” IIHR Rep. No. 232-IV, Iowa Institute of Hydraulic Research, Univ. of Iowa, Iowa City, Iowa.
Chen, H. C., and Patel, V. C.(1987). “Laminar flow at the trailing edge of a flat plate.” AIAA J., 25(7), 920–928.
Davies, A. G., and Villaret, C.(1999). “Eulerian drift induced by progressive waves above rippled and very rough beds.” J. Geophys. Res., 104(C1), 1465–1488.
Dean, R. G., and Dalrymple, R. A. (1995). Water wave mechanics for engineers and scientists, 5th reprinting, World Scientific, Singapore.
Dong, C. M. (2000). “The development of a numerical wave tank of viscous fluid and its applications.” PhD thesis, National Cheng Kung Univ., Tainan, Taiwan.
Dong, C. M., and Huang, C. J. (2001). “On a 2-D numerical wave tank in viscous fluid.” Proc., 11th Int. Offshore and Polar Engineering. Conf., Stavanger, Vol. III, 148–155.
Du Toit, C. G., and Sleath, J. F. A.(1981). “Velocity measurements close to rippled beds in oscillatory flow.” J. Fluid Mech., 112, 77–96.
Hara, T., and Mei, C. C.(1990a). “Centrifugal instability of an oscillatory flow over periodic ripples.” J. Fluid Mech., 217, 1–32.
Hara, T., and Mei, C. C.(1990b). “Oscillating flows over periodic ripples.” J. Fluid Mech., 211, 183–209.
Horikawa, K., and Watanabe, A. (1968). “Laboratory study on oscillatory boundary layer.” Proc., 11th Int. Conf. on Coastal Engineering, ASCE, New York, 467–486.
Huang, C. J., and Dong, C. M.(2001). “On the interaction of a solitary wave and a submerged dike.” Coastal Eng., 43, 265–286.
Huang, C. J., Zhang, E. C., and Lee, J. F.(1998). “Numerical simulation of nonlinear viscous wavefields generated by a piston-type wavemaker.” J. Eng. Mech., 124(10), 1110–1120.
Hwung, H. H., and Hwang, K. S. (1993). “Flow structures over a wavy boundary in wave motion.” Proc., 9th Symp. on Turbulent Shear Flows, Kyoto, 306.1–306.4.
Ikeda, S., Horikawa, K., Nakamura, H., and Noguchi, K.(1991). “Oscillatory boundary layer over a sand ripple model.” Coast. Eng. Japan, 34(1), 15–29.
Johnson, I. G., and Carlsen, N. A.(1976). “Experimental and theoretical investigations in an oscillatory turbulent boundary layer.” J. Hydraul. Res., 14(1), 45–59.
Kakinoki, T., Takikawa, K., and Yamada, F. (1999). “Characteristics of the turbulent boundary layer along sand-ripples under regular waves.” Proc., 9th Int. Offshore and Polar Engineering Conf., Brest, Vol. III, 767–774.
Kaneko, A., and Honji, H.(1979). “Double structures of steady streaming in the oscillatory viscous flow over a wavy wall.” J. Fluid Mech., 93, 727–736.
Lyne, W. H.(1971). “Unsteady viscous flow over a wavy wall.” J. Fluid Mech., 50, 33–48.
Madsen, O. S.(1971). “On the generation of long waves.” J. Geophys. Res., 76(36), 8672–8683.
Matsunaga, N., Kaneko, A., and Honji, H.(1981). “A numerical study of steady streamings in oscillatory flow over a wavy wall.” J. Hydraul. Res. 19(1), 29–42.
Nakato, T., Kennedy, J. F., Glover, J. R., and Locher, F. A.(1977). “Wave entrainment of sediment from rippled beds.” J. Waterway, Port, Coastal, Ocean Eng., 103, 83–99.
Patankar, S. V. (1980) Numerical heat transfer and fluid flow, McGraw-Hill, New York.
Ranasoma, K. I. M., and Sleath, J. F. A.(1993). “Velocity measurements close to the rippled beds.” Coastal Eng., 1992, 2383–2396.
Sato, S., Mimura, N., and Watanabe, A.(1985). “Oscillatory boundary layer flow over rippled beds.” Coastal Eng., 1984, 2293–2309.
Sato, S., Shimosako, K., and Watanabe, A.(1987). “Measurements of oscillatory boundary layer flows above ripples with a laser-Doppler velocimeter.” Coast. Eng. Japan, 30(1), 89–98.
Sawamoto, M., Yamashita, T., and Kitamura, T.(1983). “Measurements of turbulence over vortex ripple.” Coastal Eng. 1982, 282–296.
Scandura, P., Vittori, G., and Blondeaux, P.(2000). “Three-dimensional oscillatory flow over steep ripples.” J. Fluid Mech., 412, 355–378.
Sleath, J. F. A.(1974). “Stability of laminar flow at seabed.” J. Waterway, Port, Coastal, Ocean Eng., 100(2), 105–122.
Sleath, J. F. A.(1975). “A contribution to the study of vortex ripples.” J. Hydraul. Res., 13(3), 315–328.
Thompson, J. F., Warsi, Z. U. A., and Matson, C. W. (1985). Numerical grid generation, Elsevier, New York.
Toue, T., Nadaoka, K., and Katsui, H.(1997). “Asymmetric boundary layer flow above sand ripples under progressive waves.” Coastal Eng., 1996, 3183–3193.
Tunstall, E. B., and Inman, D. L.(1975). “Vortex generation by oscillatory flow over rippled surfaces.” J. Geophys. Res., 80(24), 3475–3484.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 128 • Issue 5 • September 2002
Pages: 190 - 201
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Nov 17, 2000
Revised: Apr 16, 2002
Published online: Aug 15, 2002
Published in print: Sep 2002
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.