Harter, R. and Abrahams, I. David and Simon, M. J.
(2007)
*The effect of surface tension on trapped modes in water-wave problems.*
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463 (2088).
pp. 3131-3149.
ISSN 1471-2946
(In Press)

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## Abstract

In this paper the effect of surface tension is considered on two two-dimensional water-wave problems involving pairs of immersed bodies. Both models, having fluid of infinite depth, support localized oscillations, or trapped modes, when capillary effects are excluded. The first pair of bodies is surface-piercing whereas the second pair is fully submerged. In the former case it is shown that the qualitative nature of the streamline shape is unaffected by the addition of surface tension in the free surface condition, no matter how large this parameter becomes. The main objective of this paper, however, is to study the submerged body problem. For this case it is found, by contrast, that there exists a critical value of the surface tension above which it is no longer possible to produce a completely submerged pair of bodies which support trapped modes. This critical value varies as a function of the separation of the two bodies. It can be inferred from this that surface tension does not always play a qualitatively irrelevant role in the linear water-wave problem.

Item Type: | Article |
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Uncontrolled Keywords: | water waves, trapped modes, surface tension, submerged body, localized oscillations |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 26 Nov 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/962 |

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