Generation of Long Waves in Laboratory
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 116, Issue 2
Abstract
A consistent theory is presented for generating arbitrary, finite‐amplitude, long waves at any location in a two‐dimensional, constant‐depth wave tank using a vertical paddle‐type wavemaker. The theory consists of solving an inverse evolution problem of the Korteweg‐de Vries equation; given specific initial data the boundary motion that produces that data is determined. The theory also suggests the appropriate method for calculating the force on the wavemaker. Application of this theory allows for the laboratory generation of very detailed single waveforms at arbitrary lengths away from the wave‐maker; this formalism obliterates the limitations of the existing shallow‐water wavemaker algorithms which can only reproduce wave motions either of periodic or of constant form. A series of laboratory experiments is described where relatively arbitrary single waves are specified as initial data, the theory calculates the correct boundary motion, the waves are generated and then compared with the initial data as appropriate. The experiments also demonstrate the limitations of this theory, which, even though capable of generating the leading wave emerging after a long wave breaks, it cannot model the details of the tail of the breaking wave.
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References
1.
Ablowitz, M. J., et al. (1974). “The inverse scattering transform—Fourier analysis for nonlinear problems.” Studies in Appl. Math., 53(4), 249–315.
2.
Barthel, V., et al. (1983). “Group bounded long waves in physical models.” Oc. Engrg., 10(4), 261–294.
3.
Biesel, F., and Suquet, F. (1951). “Laboratory wave generating apparatus.” Project Report 39, St. Anthony Falls Hydr. Lab., Univ. of Minnesota, Minneapolis, Minn.
4.
Chwang, A. T. (1981). “Effect of stratification on hydrodynamic pressures on dams.” J. Engrg. Math., 15(1), 49–63.
5.
Chwang, A. T. (1983). “Nonlinear hydrodynamic pressure on an accelerating plate.” Phys. Fluids, 26, 383–387.
6.
Chu, C. K., Xiang, L. W., and Baransky, Y. (1983). “Solitary waves induced by boundary motion.” Comm. Pure & Appl. Math., 36, 495–504.
7.
Courant, R., Friedrichs, K. O., and Lewy, H. (1928). “Uber die partiellen Differenzengleichungen der mathematischen Physik.” Math. Ann. West Germany, 100, 32–48.
8.
Dodd, R. K., et al. (1982). Solutions and nonlinear wave equations. Academic Press, New York, N.Y.
9.
Flick, R. E., and Guza, R. T. (1980). “Paddle generated waves in laboratory channels.” J. Waterways Port, Coast, and Ocean Div., ASCE, 106(1), 79–97.
10.
Gardner, C. S., et al. (1967). “Method for solving the Kortweg‐de Vries equation.” Phys. Rev. Letters, 19, 1095–1097.
11.
Gilbert, G., Thompson, D. M., and Brewer, A. J. (1971). “Courbes de calcul pour batteurs de houle reguliere et aleatoire.” J. Hydr. Res., 9, 163–168.
12.
Goring, D. G. (1978). “Tsunamis—the propagation of long waves onto a shelf,” thesis presented to the California Institute of Technology, at Pasadena, Calif., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
13.
Havelock, T. H. (1929). “Forced surface waves on water.” Phil. Mag., 8, 569–576.
14.
Hammack, J. L., and Segur, H. (1974). “The Korteweg‐de Vries equation and water waves. Part 2. Comparison with experiments.” J. Fluid Mech., 65, 289–314.
15.
Kennard, E. H. (1949). “Generation of waves by moving partitions.” JMM, 7, 303–312.
16.
Kim, S. K., Liu, P. L.‐F., and Ligett, J. A. (1983). “Boundary integral equation solutions for solitary wave generation, propagation and runup.” Coast. Engrg., 1, 299–317.
17.
Madsen, O. S., Mei, C. C., and Savage, R. P. (1970). “The evolution of time‐periodic long waves of finite amplitude.” J. Fluid Mech., 44, 195–208.
18.
Madsen, O. S. (1971). “On the generation of long waves.” J. Geophys. Res., 76(36), 8672–8683.
19.
Peregrine, D. H. (1966). “Calculations of the development of an undular bore.” J. Fluid Mech., 25, 321–330.
20.
Peregrine, D. H. (1967). “Long waves on a beach.” J. Fluid Mech., 27, 815–827.
21.
Richtmeyer, R. D., and Morton, K. W. (1967). Difference methods for initial value problems, John Wiley and Sons, New York, N.Y., 262 and 323.
22.
Scott‐Russel, J. (1844). On Waves. British Association for the Advancement of Science, London, England, 311–390.
23.
Segur, H. (1973). “The Korteweg‐de Vries equation and water waves. Part 1. Solutions of the equation.” J. Fluid Mech., 59, 721–736.
24.
Sand, S. E. (1982). “Long wave problems in laboratory models.” J. Waterways, Port, Coast, and Oc. Div, ASCE, 108(4), 492–503.
25.
Svendsen, I. A. (1974). “Cnoidal waves over a gently sloping bottom,” thesis presented to the Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, at Lyngby, Denmark, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
26.
Synolakis, C. E. (1986). “The runup of long waves,” thesis presented to the California Institute of Technology, at Pasadena, Calif., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
27.
Synolakis, C. E. (1987). “The runup of solitary waves.” J. Fluid Mech., 185, 523–545.
28.
Synolakis, C. E. (1989). “On determining the hydrodynamic force on an accelerating plate in a fluid with a free surface.” J. Engrg. Mech., ASCE, 115(11), 2480–2492.
29.
Ursell, F., Dean, R. G., and Yu, Y. S. (1963). “Forced small amplitude water waves: A comparison of theory and experiment.” J. Fluid Mech., 7, 33–52.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 116 • Issue 2 • March 1990
Pages: 252 - 266
Copyright
Copyright © 1990 ASCE.
History
Published online: Mar 1, 1990
Published in print: Mar 1990
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