Numerical Simulations of Nonlinear Short Waves Using a Multilayer Model
Publication: Journal of Engineering Mechanics
Volume 131, Issue 3
Abstract
The multilayer model developed by Lynett and Liu is used for simulating the evolution of deep-water waves in a constant depth. The computational model is tested with experimental data for nonlinear monochromatic and biharmonic waves with values as high as 8.3. The experiments were conducted in a super wave tank with dimensions of located at Tainan Hydraulics Laboratory of National Cheng-Kung University. The nonlinearity of the waves tested, , range from 0.0627 to 0.1577. The overall comparisons between the multilayer model and the experiments are quite good, indicating that the multilayer model is adequate for both linear and nonlinear deep-water waves.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research reported here is partially supported by Grants from National Science Foundation (CMS-9528013, CTS-9808542, and CMS 9908392). The writers would also like to acknowledge the grant to National Cheng-Kung University from the Ministry of Education of Taiwan under the Program for Promoting University Academic Excellence (A-91-E-FA09-7-3).
References
Agnon, Y., Madsen, P. A., and Schaffer, H. (1999). “A new approach to high-order Boussinesq models.” J. Fluid Mech., 399, 319–333.
Bliven, L. F., Huang, N. E., and Long, S. R. (1986). “Experimental study of the influence of wind on Benjamin-Feir sideband instability.” J. Fluid Mech., 162, 237–260.
Bonmarin, P., and Ramamonjiarisoa, A. (1985). “Deformation to breaking of deep water gravity waves.” Exp. Fluids, 3, 11–16.
Gobbi, M. F., Kirby, J. T., and Wei, G. (2000). “A fully nonlinear Boussinesq model for surface waves. II: Extension to .” J. Fluid Mech., 405, 182–210.
Israeli, M., and Orszag, S. A. (1981). “Approximation of radiation boundary conditions.” J. Comput. Phys., 41, 113–115.
Kirby, J. T., Wei, G., Chen, Q., Kennedy, A. B., and Dalrymple, R. A. (1998). FUNWAVE 1.0. Fully nonlinear Boussinesq wave model. Documentation and user’s manual, Univ. of Delaware, Del.
Lake, B. M., Yuen, H. C., Rungaldier, H., and Ferguson, W. E. (1977). “Nonlinear deep-water waves; theory and experiment. II: Evolution of a continuous wave train.” J. Fluid Mech., 83, 49–74.
Lee, C., Cho, Y.-S., and Yum, K. (2001). “Internal generation of waves for extended Boussinesq equations.” Coastal Eng., 42, 155–162.
Liu, P. L.-F. (1994). “Model equations for wave propagation from deep to shallow water.” Advances in coastal engineering, World Scientific, Singapore, Vol. 1, p. 125–157.
Lynett, P. (2002). “A multilayer approach to modeling nonlinear, dispersive waves from deep water to the shore.” PhD thesis, Cornell Univ., Ithaca, N.Y.
Lynett, P., and Liu, P. L.-F. (2004a). “A two-layer approach to wave modeling.” Proc. R. Soc. London, Ser. A, 460, 2637–2669.
Lynett, P., and Liu, P. L.-F. (2004b). “Linear analysis of the multilayer model.” Coastal Eng., in press.
Madsen, P. A., and Sorensen, O. R. (1992). “A new form of the Boussinesq equations with improved linear dispersion characteristics. II: A slowly varying bathymetry.” Coastal Eng., 18, 183–204.
Madsen, P. A., Bingham, H. B., and Liu, H. (2002). “A new Boussinesq method for fully nonlinear waves from shallow to deep water.” J. Fluid Mech., 462, 1–30.
Melville, W. K. (1982). “The instability and breaking of deep-water waves.” J. Fluid Mech., 115, 165–185.
Melville, W. K. (1983). “Wave modulation and breakdown.” J. Fluid Mech., 128, 489–506.
Nwogu, O. (1993). “Alternative form of Boussinesq equations for nearshore wave propagation.” J. Waterw., Port, Coastal, Ocean Eng., 119(6), 618–638.
Peregrine, D. H. (1967). “Long waves on a beach.” J. Fluid Mech., 27, 815–827.
Ramamonjiarisoa, A., and Mollo-Christensen, J. A. (1979). “Modulation characteristics of sea surface waves.” J. Geophys. Res., C: Oceans Atmos., 84, 7769–7775.
Su, M. Y. (1982). “Three-dimensional deep-water waves. 1: Experimental measurement of skew and symmetric wave patterns.” J. Fluid Mech., 124, 73–108.
Su, M. Y., Bergin, M., Marler, P., and Myrick, R. (1982). “Experiments on nonlinear instabilities and evolution of steep gravity-wave trains.” J. Fluid Mech., 124, 45–72.
Tulin, M. P., and Waseda, T. (1999). “Laboratory observations of wave group evolution, including breaking effects.” J. Fluid Mech., 378, 197–232.
Wei, G., and Kirby, J. T. (1995). “A time-dependent numerical code for extended Boussinesq equations.” J. Waterw., Port, Coastal, Ocean Eng., 121(5), 251–261.
Wei, G., Kirby, J. T., Grilli, S. T., and Subramanya, R. (1995). “A fully nonlinear Boussinesq model for surface waves. Part I. Highly nonlinear unsteady waves.” J. Fluid Mech., 294, 71–92.
Wei, G., Kirby, J. T., Grilli, S. T., and Sinha, A. (1999). “Generation of waves in Boussinesq models using a source function method.” Coastal Eng., 36, 271–299.
Wu, T. Y. (1981). “Long waves in ocean and coastal waters.” J. Eng. Mech. Div., 107(3), 501–522.
Information & Authors
Information
Published In
Copyright
© 2005 ASCE.
History
Received: Feb 23, 2004
Accepted: Aug 5, 2004
Published online: Mar 1, 2005
Published in print: Mar 2005
Notes
Note. Associate Editor: Michelle H. Teng
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.