Experiments and Numerics of Bichromatic Wave Groups
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 127, Issue 6
Abstract
This paper reports on extensive experiments on nonlinear wave groups that evolve in a hydrodynamic laboratory over long distances (200 m) from the generation of simple bichromatic waves. The deepwater experiments show large deformations of the wave group, with large increase of wave heights, depending on the value for the quotient of wave amplitude and frequency difference. The experimental results show little dissipation and reflections are virtually absent. A very efficient and accurate numerical code based on the full nonlinear surface wave equations, which has been developed for this purpose, reconstructs the experiments and enables one to investigate the evolution over much longer distances (reported here until 1,200 m) than in the laboratory.
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References
1.
Benjamin, T. B., and Feir, J. E. ( 1967). “The disintegration of wave trains in deep water. Part 1. Theory.” J. Fluid Mech., Cambridge, U.K., 27, 417.
2.
Chu, V. H., and Mei, C. C. ( 1970). “On slowly varying Stokes waves.” J. Fluid Mech., Cambridge, U.K., 41, 873.
3.
Chu, V. H., and Mei, C. C. ( 1971). “The nonlinear evolution of Stokes waves in deep water.” J. Fluid Mech., Cambridge, U.K., 47, 337.
4.
Greaves, D. M., Borthwick, A. G. L., Wu, G. X., and Eatock Taylor, R. ( 1997). “A moving boundary finite element method for fully nonlinear wave simulations.” J. Ship Res., 41(3), 181–194.
5.
Hasimoto, H., and Ono, H. ( 1972). “Nonlinear modulation of gravity waves.” J. Phys. Soc. Japan, 33, 805.
6.
Krasitskii, V. P. ( 1994). “On reduced equations in the hamiltonian theory of weakly nonlinear surface waves.” J. Fluid Mech., Cambridge, U.K., 272, 1.
7.
Lo, E., and Mei, C. C. ( 1985). “A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation.” J. Fluid Mech., Cambridge, U.K., 150, 395.
8.
Pelinovsky, E., Talipova, T., Kit, E., and Etian, O. ( 1999). “Nonlinear wave packet evolution in shallow water.” Proc., Int. Symp. on Progress in Coast. Engrg. and Oceanography, 53–60.
9.
Schäffer, H. A. ( 1996). “Second-order wavemaker theory for irregular waves.” Oc. Engrg., 23, 47–88.
10.
Shemer, L., Kit, E., Jiao, H., and Etian, O. (1998). “Experiments on nonlinear wave groups in intermediate water depth.”J. Wtrwy., Port, Coast. and Oc. Engrg., ASCE, 124(6), 320–327.
11.
Stansberg, C. ( 1997). “On the nonlinear behaviour of ocean wave groups.” Proc., Waves '97, Vol. 2, 1227–1241.
12.
Stiassnie, M., and Kroszynski, U. I. ( 1982). “Long-time evolution of an unstable water-wave train.” J. Fluid Mech., Cambridge, U.K., 116, 207–225.
13.
van Groesen, E. ( 1998). “Wave groups in uni-directional surface wave models.” J. Engrg. Mathematics, 34, 215–226.
14.
van Groesen, E., Andonowati, A., and Soewono, E. ( 1999). “Nonlinear effects in bichromatic surface waves.” Proc., Estonian Acad., Sci. Phys. Mathematics, 48, 206–229.
15.
van Groesen, E., Cahyono, E., and Surganko, A. ( 2001). “Uni-directional models for narrow and broadband pulse propagation in second-order nonlinear media.” J. Optics Quantum Electonics (in press).
16.
Westhuis, J. ( 2001). “The numerical simulation of nonlinear waves in a hydrodynamic model test basin.” PhD thesis, University of Twente, Enschede, The Netherlands.
17.
Westhuis, J., and Huijsmans, R. H. M. ( 1999). “Unstable bichromatic wave groups: Experimental results.” Tech. Rep. 15309.152, Maritime Research Institute Netherlands, Wageningen, The Netherlands.
18.
Westhuis, J., van Groesen, E., and Huijsmans, R. H. M. ( 2000). “Long time evolution of unstable bichromatic waves.” Proc., 15th IWWW&FB, T. Miloh, ed.
19.
Yuen, H. C., and Lake, B. M. ( 1975). “Nonlinear deep water waves: Theory and experiment.” Phys. Fluids, 18, 956.
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Received: May 24, 2000
Published online: Dec 1, 2001
Published in print: Dec 2001
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