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On the Existence of Trapped Modes in Channels of Arbitrary Cross-section

✍ Scribed by M. D. Groves

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
356 KB
Volume
20
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by F. Ursell

This article establishes the existence of trapped-mode solutions of a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls. A trapped mode corresponds to an eigenvalue of a non-local Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by generalizing previous results concerning spectral theory for differential operators to this non-local operator.

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