Numerical Generation and Absorption of Fully Nonlinear Periodic Waves
Publication: Journal of Engineering Mechanics
Volume 123, Issue 10
Abstract
Permanent form periodic waves with zero-average mass flux are generated in a two-dimensional numerical wave tank solving fully nonlinear potential flow equations. An absorbing beach is modeled at the end of the tank in which (1) an external free-surface pressure absorbs energy from high frequency waves; and (2) a pistonlike condition absorbs energy from low-frequency waves. A feedback mechanism adaptively calibrates the beach parameters to absorb the period-averaged energy of incident waves. Wave generation and absorption are validated over constant depth, for tanks and beaches of various lengths, and optimal parameter values are identified for which reflection from the beach is reduced to a few percent. Shoaling of periodic waves is then modeled over a 1:50 slope, up to very close to the breaking point. A quasi-steady state is reached in the tank for which (not previously calculated) characteristics of fully nonlinear shoaling waves are obtained.
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References
1.
Brebbia, C. A. (1978). The boundary element method for engineers. John Wiley & Sons, London, U.K.
2.
Brorsen, M., and Larsen, J.(1987). “Source generation of nonlinear gravity waves with the boundary integral method.”Coast. Engrg., 11, 93–113.
3.
Cao, Y., Beck, R. F., and Schultz, W. W. (1993). “An absorbing beach for numerical simulations of nonlinear waves in a wave tank.”Proc., Eighth Int. Workshop Water Waves and Floating Bodies, 17–20.
4.
Chapalain, G., Cointe, R., and Temperville, A.(1996). “Observed and modeled resonantly interacting progressive water-waves.”Coast. Engrg., 16, 267–300.
5.
Clément, A.(1996). “Coupling of two absorbing boundary conditions for 2D time-domain simulations of free surface gravity waves.”J. Comp. Phys., 126, 139–151.
6.
Cointe, R.(1990). “Numerical simulation of a wave channel.”Engrg. Anal. with Boundary Elements, 7(4), 167–177.
7.
Cooker, M. J.(1990). “A boundary-integral method for water wave motion over irregular bed.”Engrg. Anal. with Boundary Elements, 7(4), 205–213.
8.
Dalrymple, R. A.(1976). “Wave-induced mass transport in water waves.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 102(2), 255–264.
9.
Dean, R. G., and Dalrymple, R. A. (1984). Water wave mechanics for engineers and scientists. Prentice-Hall, Englewood Cliffs, N.J.
10.
Dold, J. W., and Peregrine, D. H. (1986). “An efficient boundary integral method for steep unsteady water waves.”Numerical methods for fluid dynamics II, K. W. Morton and M. J. Baines, eds., Clarendon Press, Oxford, U.K., 671–679.
11.
Dommermuth, D. G., Yue, D. K. P., Lin, W. M., Rapp, R. J., Chan, E. S., and Melville, W. K.(1988). “Deep-water plunging breakers: A comparison between potential theory and experiments.”J. Fluid Mech., 189, 423–442.
12.
Engquist, B., and Majda, A.(1977). “Absorbing boundary conditions for the numerical simulation of waves.”Math. Comp., 31, 629–651.
13.
Grilli, S. T., and Horrillo, J. (1997). “Nonlinear properties of waves shoaling over slopes and natural beaches.”Proc., 25th Int. Conf. on Coast. Engrg., Vol. 1, ASCE, New York, N.Y., 717–730.
14.
Grilli, S. T., Skourup, J., and Svendsen, I. A.(1989). “An efficient boundary element method for nonlinear water waves.”Engrg. Anal. with Boundary Elements, 6(2), 97–107.
15.
Grilli, S. T., and Subramanya, R.(1994). “Quasi-singular integrations in the modelling of nonlinear water waves.”Engrg. Anal. with Boundary Elements, 13(2), 181–191.
16.
Grilli, S. T., and Subramanya, R.(1996). “Numerical modeling of wave breaking induced by fixed or moving boundaries.”Comp. Mech., 17, 374–391.
17.
Grilli, S. T., Subramanya, R., Svendsen, I. A., and Veeramony, J.(1994). “Shoaling of solitary waves on plane beaches.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 120(6), 609–628.
18.
Grilli, S. T., and Svendsen, I. A.(1990). “Corner problems and global accuracy in the boundary element solution of nonlinear wave flows.”Engrg. Anal. with Boundary Elements, 7(4), 178–195.
19.
Grilli, S. T., Svendsen, I. A., and Subramanya, R.(1997). “Breaking criterion and characteristics for solitary waves on plane beaches.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 123(2), 102–112.
20.
Israeli, M., and Orszag, S. A.(1981). “Approximation of radiation boundary conditions.”J. Comp. Phys., 41, 115–135.
21.
Klopman, G. (1988). “Numerical simulation of gravity wave motion on steep slopes.”Delft Hydr. Rep. No. H195, Delft, The Netherlands.
22.
Larsen, J., and Dancy, H.(1983). “Open boundaries in short waves simulations—A new approach.”Coast. Engrg., 7, 285–297.
23.
Le Mehauté, B.(1972). “Progressive wave absorber.”J. Hydr. Res., 10(2), 153–169.
24.
Lin, W. M., Newman, J. N., and Yue, D. K. (1984). “Nonlinear forced motion of floating bodies.”Proc., 15th Int. Symp. on Naval Hydrodynamics, Hamburg, Germany.
25.
Longuett-Higgins, M. S., and Cokelet, E. D. (1976). “The deformation of steep surface waves on water—I. A numerical method of computation.”Proc., Royal Soc. London, London, U.K., A350, 1–26.
26.
Mansard, E. P., and Funke, E. R. (1980). “The measurement of incident and reflected spectra using a least square method.”Proc., 17th Int. Conf. on Coast. Engrg., Vol. 1, ASCE, New York, N.Y., 154–172.
27.
Mei, C. C. (1989). The applied dynamics of ocean surface waves, Second Ed., World Scientific, River Edge, N.J.
28.
New, A. L., McIver, P., and Peregrine, D. H.(1985). “Computation of overturning waves.”J. Fluid Mech., 150, 233–251.
29.
Ohyama, T., and Nadaoka, K.(1991). “Development of a numerical wave tank for analysis of nonlinear and irregular wave fields.”Fluid Dynamic Res., 8, 231–251.
30.
Ohyama, T., and Nadaoka, K.(1994). “Transformation of a nonlinear wave train passing over a submerged shelf without breaking.”Coast. Engrg., 24, 1–22.
31.
Orlanski, I.(1976). “A simple boundary condition for unbounded hyperbolic flows.”J. Comp. Phys., 21, 251–269.
32.
Otta, A. K., Svendsen, I. A., and Grilli, S. T. (1992). “Unsteady free surface waves in region of arbitrary shape.”CACR, Res. Rep. 92-10, Univ. of Delaware, Newark, Del.
33.
Romate, J.(1992). “Absorbing boundary conditions for free surface waves.”J. Comp. Phys., 99, 135–145.
34.
Schäffer, H. A.(1996). “Second-order wavemaker theory for irregular waves.”Oc. Engrg., 23, 47–88.
35.
Sommerfeld, A. (1949). Partial differential equations in physics. Academic Press, New York, N.Y.
36.
Subramanya, R., and Grilli, S. T. (1994). “Kinematics and properties of fully nonlinear waves shoaling and breaking over a gentle slope.”Proc., Int. Symp. on Waves—Phys. and Numer. Modeling, M. Isaacson and M. Quick, eds., IAHR, 1106–1115.
37.
Svendsen, I. A., and Grilli, S. T.(1990). “Nonlinear waves on steep slopes.”J. Coast. Res., 7, 185–202.
38.
Vinje, T., and Brevig, P. (1981). “Numerical simulation of breaking waves.”Adv. Water Res., 4, 77–82
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 123 • Issue 10 • October 1997
Pages: 1060 - 1069
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Oct 1, 1997
Published in print: Oct 1997
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