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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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