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Nazarov, S.A., Ruotsalainen, K.M. Curved channels with constant cross sections may support trapped surface waves. Z. Angew. Math. Phys. 74, 149 (2023). https://doi.org/10.1007/s00033-023-02048-z

Curved channels with constant cross sections may support trapped surface waves

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Author: Nazarov, Sergei A.1; Ruotsalainen, Keijo M.2
Organizations: 1Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
2Applied and Computational Mathematics, University of Oulu, P.O. Box 8000, FI-90014, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.7 MB)
Persistent link: http://urn.fi/urn:nbn:fi-fe20230823103635
Language: English
Published: Springer Nature, 2023
Publish Date: 2023-08-23
Description:

Abstract

Curved channels with constant cross sections are constructed which support a trapped surface wave. Since corresponding eigenvalues are embedded in the continuous spectrum of the water wave problem and therefore possess the natural instability, the construction procedure requires “fine-tuning” of several parameters in the (small) curvature of the channel as well as geometrical restrictions on the cross section. In particular, the mirror symmetry of the cross section with respect to the vertical axis disrupts the procedure, but examples of suitable non-symmetric cross sections are provided.

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Series: Zeitschrift für angewandte Mathematik und Physik
ISSN: 0044-2275
ISSN-E: 1420-9039
ISSN-L: 0044-2275
Volume: 74
Issue: 4
Article number: 149
DOI: 10.1007/s00033-023-02048-z
OADOI: https://oadoi.org/10.1007/s00033-023-02048-z
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
Asymptotic analysis
Augmented scattering matrix
Embedded eigenvalues
Trapped modes
Water waves
Waveguides
Article
Funding: This work was completed with the support of Academy of Finland (Grant nr. 343220: Researchers’ mobility to Finland).
Academy of Finland Grant Number: 343220
Detailed Information: 343220 (Academy of Finland Funding decision)
Copyright information: © 2023 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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