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Trapped modes in a fluid with three layers topped by a rigid lid

Trapped modes in a fluid with three layers topped by a rigid lid

Mathematical Methods in the Applied Sciences

Filipe S. Cal; Gonçalo A. S. Dias; Bruno M.A.M. Pereira — 2022

Key information

Authors:

Filipe S. Cal (Filipe Santiago Cal); Gonçalo A. S. Dias (Gonçalo Apra Sardinha Cunha Dias); Bruno M.A.M. Pereira (Bruno Miguel Almeida Martins Pereira)

Published in

May 6, 2022

Abstract

<jats:p>We consider trapping of linear water waves by a submerged horizontal cylinder in a three‐layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary‐value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given.</jats:p>

Publication details

Authors in the community:

Publication version

AO - Author's Original

Title of the publication container

Mathematical Methods in the Applied Sciences

First page or article number

9928

Last page

9944

Volume

45

Issue

16

ISSN

1099-1476

DOI

10.1002/mma.8347

Fields of Science and Technology (FOS)

mathematics - Mathematics

Publication language (ISO code)

eng - English

Alternative identifier (URI)

http://dx.doi.org/10.1002/mma.8347

Rights type:

Restricted access