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Eigenmodes in the water-wave problems for infinite pools with cone-shaped bottom

Published online by Cambridge University Press:  13 July 2016

Mikhail A. Lyalinov
Mikhail A. Lyalinov*
Affiliation:
Department of Mathematical Physics, Physics Faculty, Saint-Petersburg University, 7/9 Universitetskaya nab., Saint-Petersburg, 199034, Russia
*
†Email addresses for correspondence: lyalinov@yandex.ru, m.lyalinov@spbu.ru
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Abstract

In the framework of the assumptions of the linearized theory of small-amplitude water waves, the eigenfunctions of the point spectrum are studied for boundary-value problems in infinite domains. Special types of three-dimensional infinite water pools characterised by cone-shaped bottoms are considered. By means of an incomplete separation of variables and exploiting the Mellin transform, we reduce construction of the eigenmodes to the study and solution of the problems for some functional difference equations with meromorphic coefficients. The behaviour of the eigenmodes at a singular point of the boundary and the rate of their decay at infinity are also examined.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 800 , 10 August 2016 , pp. 645 - 665
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Copyright
© 2016 Cambridge University Press 

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