✦ LIBER ✦

Trapped-mode solutions for gravity-capillary water waves in channels of arbitrary cross-section

✍ Scribed by M. D. Groves

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 167 KB
Volume: 21
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(19980525)21:8<701::aid-mma967>3.0.co;2-d

No coin nor oath required. For personal study only.

✦ Synopsis

Communicated by F. Ursell

This article establishes the existence of a trapped-mode solution to 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; the forces of gravity and surface tension are operative. A trapped mode corresponds to an eigenvalue of the composition of an inverse differential operator and a Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by extending previous results dealing with the case when surface tension is absent.

📜 SIMILAR VOLUMES

Resonance phenomena for water waves in c

Resonance phenomena for water waves in channels of arbitrary cross-section

✍ M. D. Groves; P. H. Lesky 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 284 KB

## 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 fre

On the Existence of Trapped Modes in Cha

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

✍ M. D. Groves 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 356 KB

## 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