Generation and Propagation of Water Waves in a Two-Dimensional Numerical Viscous Wave Flume
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 130, Issue 3
Abstract
This study investigated the generation and propagation of water waves in a numerical viscous wave flume. The numerical scheme developed by Huang and collaborators for solving the unsteady two-dimensional Navier–Stokes equations for wavemaking problems was employed to generate different incident waves, including small- and finite-amplitude waves and solitary waves. The accuracy of the numerical results for the wave and velocity profiles was verified by comparison with the analytical solutions. The wave propagation in a numerical wave flume was also investigated. For periodic gravity waves on finite water depth, the results showed that waves with larger Ursell numbers are more stable than those with smaller Ursell numbers. The propagation of solitary waves in the channel is stable. For stable waves, the wave height attenuation caused by the energy dissipation in the wave motion was shown to be consistent with the theoretical results.
Get full access to this article
View all available purchase options and get full access to this article.
References
Benjamin, T. B.(1967). “Instability of periodic wave trains in non-linear dispersive system.” Proc. R. Soc. London, Ser. A, 299, 59–75.
Benjamin, T. B., and Feir, J. E.(1967). “The disintegration of wave trains on deep water, Part 1. Theory.” J. Fluid Mech., 27, 417–430.
Biesel, F., and Suquet, F. (1954). “Laboratory wave-generating apparatus.” Project Rep. No. 39, St. Anthony Falls Hydraulic Laboratory, Univ. of Minnesota, Minn.
Buhr Hansen, J., and Svendsen, I. A. (1974). “Regular waves in shoaling water: experimental data.” Series Paper 21, ISVA Technical Univ., Denmark.
Chen, C. J., and Chen, H. C. (1982). “The finite-analytic method.” IIHR Rep. No. 232-IV, Iowa Inst. 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, 920–928.
Clement, A. H. (1999). “Benchmark test cases for numerical wave absorption: 1st workshop of ISOPE numerical wave tank group.” Proc., 9th Int. Offshore and Polar Engineering Conf., ISOPE, Brest, 3, 266–289.
Dean, R. G., and Dalrymple, R. A. (1984). Water wave mechanics for engineers and scientists, Prentice-Hall, Englewood Cliffs, N.J.
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.
Flick, R. E., and Guza, R. T.(1980). “Paddle generated waves in laboratory channels.” J. Waterw. Port, Coastal Ocean Div., Am. Soc. Civ. Eng., 106(1), 79–97.
Fontanet, P.(1961). “Theorie de la generation de la houl cylindrique par un batteur plan.” Houille Blanche, 16, 3–31.
Gentaz, L., Maury, C., Alessandrini, B., and Delhommeau, G. (1998). “Numerical simulation of a two-dimensional wave tank in viscous fluid.” Proc., 8th Int. Offshore and Polar Engineering Conf., ISOPE, Montréal, 256–263.
Goda, Y. (1967). “Travelling secondary wave crests in wave channels.” Rep. No. 13, Port & Harbor Research Inst., 32–38.
Goring, D., and Raichlen, F. (1980). “The generation of long waves in the laboratory.” Proc., 17th Coastal Eng. Conf., ASCE, New York, 763–783.
Grilli, S. T., and Horrillo, J.(1997). “Numerical generation and absorption of fully nonlinear periodic waves.” J. Eng. Mech., 123(10), 1060–1069.
Havelock, T. H.(1929). “Forced surface wave on water.” Philos. Mag., 7(8), 569–576.
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 piston-type wavemaker.” J. Eng. Mech., 124(10), 1110–1120.
Hudspeth, R. T., Leonard, J. W., and Chen, M. C.(1981). “Design curves for hinged wavemakers: Experiments.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(5), 553–574.
Hughes, S. A. (1993). Physical models and laboratory techniques in coastal engineering, Chap. 7, World Scientific, Singapore.
Keulegan, G. H.(1948). “Gradual damping of solitary waves.” J. Res. Natl. Bur. Stand., 40, 487–498.
Kim, M. H., Park, J. C., Hong, S. H., and Tavassoli, A. (1999). “Fully nonlinear multi-directional waves by a 3D viscous numerical wave tank.” Proc., 9th Int. Offshore and Polar Engineering Conf., ISOPE, Brest, 412–419.
Le Méhauté, B. (1969). “An introduction to hydrodynamics and water waves.” ESSA Tech. Rep. ERL 118-Pol 3-2.
Madsen, O. S.(1971). “On the generation of long waves.” J. Geophys. Res., 76, 8672–8683.
McLean, J. W.(1982a). “Instabilities of finite-amplitude water waves.” J. Fluid Mech., 114, 315–330.
McLean, J. W.(1982b). “Instabilities of finite-amplitude gravity waves on water of finite depth.” J. Fluid Mech., 114, 331–341.
Mei, C. C. (1983). The applied dynamics of ocean surface waves, Wiley, New York.
Mizuguchi, M.(1987). “Second-order solution of laminar boundary layer flow under waves.” Coast. Eng. Japan, 30, 9–18.
Ohyama, T., and Nadaoka, K.(1991). “Development of a numerical wave tank for analysis of nonlinear and irregular wave field.” Fluid Dyn. Res., 8, 231–251.
Patankar, S. V. (1980). Numerical heat transfer and fluid flow, McGraw-Hill, New York.
Skourup, J., and Schäffer, H. A. (1998). “Simulation with a 3D active absorption method in a numerical wave tank.” Proc., 8th Int. Offshore and Polar Engineering Conf., ISOPE, Montréal, 248–255.
Su, M. Y., Bergin, M., Marler, P., and Myrick, R.(1982a). “Experiments on nonlinear instabilities and evolution of steep gravity wave trains.” J. Fluid Mech., 124, 45–72.
Su, M. Y., Bergin, M., Myrick, R., and Roberts, J. (1982b). “Experiments on shallow-water wave grouping and breaking.” Proc., 1st Int. Conf. Meteorology Air–Sea Interaction Coastal Zone, The Hague, 107–112.
Svendsen, I. A. (1985). “Physical modeling of water waves.” Physical modeling in coastal engineering, R. A. Dalrymple, ed., Balkema, Rotterdam, The Netherlands, 13–47.
Ursell, F., Dean, R. G., and Yu, Y. S.(1960). “Forced small-amplitude water waves: A comparison of theory and experiment.” J. Fluid Mech., 7, 32–53.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 130 • Issue 3 • May 2004
Pages: 143 - 153
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Oct 22, 2002
Accepted: Oct 20, 2003
Published online: Apr 15, 2004
Published in print: May 2004
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.