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Standing waves, localised near the shoreline of a water basin, and asymptotic quasimodes

Published online by Cambridge University Press:  31 May 2024

Mikhail A. Lyalinov Open the ORCID record for Mikhail A. Lyalinov [Opens in a new window]
Mikhail A. Lyalinov*
Affiliation:
Department of Mathematical Physics, Physics Faculty, St Petersburg University, 7/9 Universitetskaya nab., St Petersburg 199034, Russia
*
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

In this work, formal asymptotic solutions of a problem for linear water waves in a bounded basin are constructed. The solutions have the form of asymptotic quasimodes and are used for the description of standing water waves localised near the shoreline. Such short-wavelength quasimodes exist only for a discrete set of frequencies, which are determined by means of a quantisation-type condition. Some numerical results are also addressed.

JFM classification

Waves/Free-surface Flows: Faraday waves Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 988 , 10 June 2024 , A22
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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