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Linear water waves: the horizontal motion of a structure in the time domain

Published online by Cambridge University Press:  10 August 2012

P. McIver
P. McIver*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 2DH, UK
*
†Email address for correspondence: [email protected]
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Abstract

The framework of the linearized theory of water waves in the time domain is used to examine the horizontal motion of an unrestrained floating structure. One of the principal assumptions of the theory is that an infinitesimal disturbance of the rest state will lead to an infinitesimal motion of the fluid and structure. It has been known for some time that for some initial conditions the theory predicts an unbounded horizontal motion of the structure that violates this assumption, but the possibility does not appear to have been examined in detail. Here some circumstances that lead to predictions of large motions are identified and, in addition, it is shown that not all non-trivial initial conditions lead to violations of the assumptions. In particular, it is shown that the horizontal motion of a floating structure remains bounded when it is initiated by the start up of a separate wave maker. The general discussion is supported by specific calculations for a vertical circular cylinder.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 289 - 312
Copyright
Copyright © Cambridge University Press 2012

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