Water Waves Over Ripples
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 112, Issue 2
Abstract
The interaction of small amplitude water waves with a patch of bottom ripples is studied using the Boundary Integral Equation Method (BIEM). Normal and oblique wave incidence is examined for reflection coefficients and the laboratory data of Davies and Heathershaw are compared to the numerical results, with the conclusion that the analytical model of Davies and Heathershaw overestimates the reflection coefficient at resonance. Comparison of BIEM results for oblique incidence is made with an extension of the recent work of Mei showing good agreement, even for large amplitude ripples.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Dalrymple, R. A., and Fowler, J. F., “Bragg Scattering by Pile‐Supported Structures,” Journal of the Waterway, Port, Coastal, and Ocean Division, ASCE, Vol. 108, No. WW3, 1982, pp. 426–429.
2.
Davies, A. D., “The Reflection of Wave Energy by Undulations on the Seabed,” Dynamics of Atmos. and Oceans, Vol. 6, 1982, pp. 207–232.
3.
Davies, A. D., “On the Interaction between Surface Waves and Undulations on the Seabed,” J. Marine Research, Vol. 40, No. 2, 1982, pp. 331–368.
4.
Davies, A. D., and Heathershaw, A. D., “Surface Wave Propagation Over Sinusoidaily Varying Topography: Theory and Observation,” Part. I, II, Report No. 159, Institute of Oceanographic Sciences, Taunton, 1983.
5.
Davies, A. D., and Heathershaw, A. D., “Surface Wave Propagation Over Sinusoidaily Varying Topography,” J. Fluid Mech., Vol. 144, 1984, pp. 419–443.
6.
Heathershaw, A. D., “Seabed‐Wave Resonance and Sand Bar Growth,” Nature, Vol. 296, No. 5855, 1982, pp. 343–345.
7.
Jaswon, M. A., and Ponter, A. R., “An Integral Equation Solution of the Torsion Problem,” Proc. Royal Society, Vol. 273, Series A, 1963, pp. 237–246.
8.
Kirby, J. T., and Dalrymple, R. A., “Propagation of Obliquely Incident Water Waves Over a Trench,” J. Fluid Mech., Vol. 133, 1983, pp. 47–63.
9.
Lamb, Sir H., Hydrodynamics, Dover Press, New York, 1945.
10.
Lennon, G. P., Liu, P. L.‐F., and Ligget, J. A., “Boundary Integral Solutions of Water Wave Problems,” Journal of the Hydraulics Division, ASCE, Vol. 108, No. HY8, 1982, pp. 921–931.
11.
Ligget, J. A., “Location of the Free Surface in Porous Media,” Journal of the Hydraulics Division, ASCE, Vol. 103, No. HY4, 1977, pp. 353–365.
12.
Liu, P. L.‐F., and Abbaspour, M., “An Integral Equation Method for the Diffraction of Oblique Waves by an Infinite Cylinder,” Int. J. Num. Methods Engrg., Vol. 18, No. 10, 1982, pp. 1497–1504.
13.
Mei, C. C., “Weak Reflection of Water Waves by Bottom Obstacles,” Journal of the Engineering Mechanics Division, ASCE, Vol. 95, No. EM1, 1969, pp. 183–194.
14.
Mei, C. C., “Resonant Reflection of Surface Water Waves by Periodic Sandbars,” J. Fluid Mech., Vol. 152, 1985, pp. 315–336.
15.
Mitra, A., and Greenberg, M., “Slow Interactions of Gravity Waves and a Corrugated Sea Bed,” J. Applied Mech., Vol. 51, 1984, pp. 251–255.
16.
Raichlan, F., and Lee, J. J., “An Inclined‐Plate Wave Generator,” Proc. 16th Int. Conf. Coastal Engrg., ASCE, Hamburg, 1978, pp. 388–399.
17.
Salmon, J. R., Liu, P. L.‐F., and Ligget, J. A., “Integral Equation Method for Linear Water Waves,” Journal of the Hydraulics Division, ASCE, Vol. 106, No. HY12, 1980, pp. 1995–2010.
18.
Yeung, R. W., “A Hybrid Integral Equation Method for Time Harmonic Free Surface Flow,” Proc. 1st Int. Conf. on Num. Ship Hydrod., 1975, pp. 581–607.
Information & Authors
Information
Published In
Copyright
Copyright © 1986 ASCE.
History
Published online: Mar 1, 1986
Published in print: Mar 1986
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.