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On the excitation of long nonlinear water waves by a moving pressure distribution

Published online by Cambridge University Press:  20 April 2006

T. R. Akylas
T. R. Akylas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A study is made of the wave disturbance generated by a localized steady pressure distribution travelling at a speed close to the long-water-wave phase speed on water of finite depth. The linearized equations of motion are first used to obtain the large-time asymptotic behaviour of the disturbance in the far field; the linear response consists of long waves with temporally growing amplitude, so that the linear approximation eventually breaks down owing to finite-amplitude effects. A nonlinear theory is developed which shows that the generated waves are actually of bounded amplitude, and are governed by a forced Korteweg-de Vries equation subject to appropriate asymptotic initial conditions. A numerical study of the forced Korteweg-de Vries equation reveals that a series of solitons are generated in front of the pressure distribution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 455 - 466
Copyright
© 1984 Cambridge University Press

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References

Debnath, L. & Rosenblat, S. 1969 Q. J. Mech. Appl. Maths. 22, 221–233.
Huang, D.-B., Sibul, O. J., Webster, W. C., Wehausen, J. V., Wu, D.-M. & Wu, T. Y. 1982 In: Proc. Conf. on Behaviour of Ships in Restricted Waters, Varna.
Peregrine, D. H. 1966 J. Fluid Mech. 25, 321–330.
Stoker, J. J. 1957 Water Waves. Interscience.
Vliegenthart, A. C. 1971 J. Engng Maths 5, 137–155.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Interscience.
Wu, D.-M. & Wu, T. Y. 1982 In Proc. 14th Symp. on Noval Hydrodyn., Ann Arbor.
Zabusky, N. J. & Kruskal, M. D. 1965 Phys. Rev. Lett. 15, 240.