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Trapping modes in the theory of surface waves

Published online by Cambridge University Press:  24 October 2008

F. Ursell
F. Ursell
Affiliation:
Department of MathematicsThe UniversityManchester
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Abstract

It is shown that a mass of fluid bounded by fixed surfaces and by a free surface of infinite extent may be capable of vibrating under gravity in a mode (called a trapping mode) containing finite total energy. Trapping modes appear to be peculiar to the theory of surface waves; it is known that there are no trapping modes in the theory of sound. Two trapping modes are constructed: (1) a mode on a sloping beach in a semi-infinite canal of finite width, (2) a mode near a submerged circular cylinder in an infinite canal of finite width. The existence of trapping modes shows that in general a radiation condition for the waves at infinity is insufficient for uniqueness.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 2 , April 1951 , pp. 347 - 358
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

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