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On the free-surface flow of very steep forced solitary waves

Published online by Cambridge University Press:  13 December 2013

Stephen L. Wade ,
Benjamin J. Binder ,
Trent W. Mattner  and
James P. Denier
Stephen L. Wade*
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
Benjamin J. Binder
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
Trent W. Mattner
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
James P. Denier
Affiliation:
Department of Engineering Science, The University of Auckland, Auckland 1142, New Zealand
*
†Email address for correspondence: stephen.wade@adelaide.edu.au
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Abstract

The free-surface flow of very steep forced and unforced solitary waves is considered. The forcing is due to a distribution of pressure on the free surface. Four types of forced solution are identified which all approach the Stokes-limiting configuration of an included angle of $12{0}^{\circ } $ and a stagnation point at the wave crests. For each type of forced solution the almost-highest wave does not contain the most energy, nor is it the fastest, similar to what has been observed previously in the unforced case. Nonlinear solutions are obtained by deriving and solving numerically a boundary integral equation. A weakly nonlinear approximation to the flow problem helps with the identification and classification of the forced types of solution, and their stability.

JFM classification

Waves/Free-surface Flows: Channel flow Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 739 , 25 January 2014 , pp. 1 - 21
Copyright
©2013 Cambridge University Press 

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