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Experiments on strong interactions between solitary waves

Published online by Cambridge University Press:  12 April 2006

P. D. Weidman and
T. Maxworthy
P. D. Weidman
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
T. Maxworthy
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
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Abstract

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Kortewegde Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 3 , 13 April 1978, pp. 417 - 431
Copyright
© 1978 Cambridge University Press

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References

Byatt-Smith, J. G. B. 1971 An integral equation for unsteady surface waves and a comment on the Boussinesq equation. J. Fluid Mech. 49, 625–633.Google Scholar
French, J. A. 1969 Wave uplift pressures on horizontal platforms. Calif. Inst. Tech., Pasadena Rep. KH-R-19.Google Scholar
Hammack, J. L. & Segur, H. 1974 The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments. J. Fluid Mech. 65, 289–314.Google Scholar
Hirota, R. 1971 Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27, 1192–1194.Google Scholar
Ippen, A. T., Kulin, G. & Raza, M. A. 1955 Damping characteristics of the solitary wave. Hydrodyn. Lab., M.I.T. Tech. Rep. no. 16.Google Scholar
Iwasa, Y. 1959 Attenuation of solitary waves on a smooth bed. A.S.C.E. Trans. 24, 193–206.Google Scholar
Keulegan, G. H. 1948 Gradual damping of solitary waves. Nat. Bur. Sci. J. Res. 40, 487–498.Google Scholar
Keulegan, G. H. 1959 Energy dissipation in standing waves in rectangular basins. J. Fluid Mech. 6, 33–50.Google Scholar
Kruskal, M. D. 1974 The Korteweg-de Vries equation and related evolution equations. Lectures in Appl. Math. vol. 15. Nonlinear Wave Motion, pp. 61–83.Google Scholar
Laitone, E. V. 1960 The second approximation to cnoidal and solitary waves. J. Fluid Mech. 9, 430–444.Google Scholar
Maxworthy, T. 1976 Experiments on collisions between solitary waves. J. Fluid Mech. 76, 177–185.Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. Roy. Soc. A 297, 459–475.Google Scholar
Miles, J. W. 1977a Damping of weakly nonlinear shallow-water waves. J. Fluid Mech. 76, 251–257.Google Scholar
Miles, J. W. 1977b Obliquely interacting solitary waves. J. Fluid Mech. 79, 157–169.Google Scholar
Oikawa, M. & Yajima, N. 1973 Interactions of solitary waves - a perturbation approach to non-linear systems. J. Phys. Soc. Japan 34, 1093–1099.Google Scholar
Whitham, G. B. 1974 Linear and Non-Linear Waves. Interscience.