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An analysis of the initial-value wavemaker problem

Published online by Cambridge University Press:  26 April 2006

S. W. Joo ,
W. W. Schultz  and
A. F. Messiter
S. W. Joo
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA
W. W. Schultz
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA
A. F. Messiter
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA
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Abstract

A Fourier-integral method is developed to obtain transient solutions to potential wavemaker problems. This method yields solutions for wavemaker velocities which need not be given as powers of time. The results are compared with known small-time and local solutions. Examples considered include ramp, step, and harmonic wavemaker velocities. As time becomes large, the behaviour near the wave front is derived for the impulsive wavemaker, and for the harmonic wavemaker it is shown that the steady-state solution is recovered. The solution for a wavemaker velocity given as a Fourier cosine series compares favourably with available experimental results. Capillary effects are included and nonlinear effects are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 161 - 183
Copyright
© 1990 Cambridge University Press

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