๐”– Bobbio Scriptorium
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Resonance phenomena for water waves in channels of arbitrary cross-section

โœ Scribed by M. D. Groves; P. H. Lesky

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
284 KB
Volume
22
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

Communicated by P. Werner

This article studies the evolutionary problem for linear gravity waves on the surface of water in a uniform, symmetric channel which is excited by an antisymmetric pressure force of frequency at the free surface. It is shown that there is a countably in"nite set of frequencies + , , . . . , which give rise to resonance phenomena: the amplitude of the wave motion grows like t as tPR in a sense which is precisely speci"ed. Under pressure forcing at any other frequency the solution obeys the principle of limiting amplitude. These results are obtained by combining methods developed for problems in acoustic waveguides with regularity theory for elliptic boundary-value problems in non-smooth domains.

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