Stability of hydroelastic waves in deep water

Blyth, Mark G., Părău, Emilian I. ORCID: https://orcid.org/0000-0001-5134-2068 and Wang, Zhan (2024) Stability of hydroelastic waves in deep water. Water Waves. ISSN 2523-3688

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Abstract

Two-dimensional periodic travelling hydroelastic waves on water of infinite depth are investigated. A bifurcation branch is tracked that delineates a family of such solutions connecting small amplitude periodic waves to the large amplitude static state for which the wave is at rest and there is no fluid motion. The stability of these periodic waves is then examined using a surface-variable formulation in which a linearised eigenproblem is stated on the basis of Floquet theory and solved numerically. The eigenspectrum is discussed encompassing both superharmonic and subharmonic perturbations. In the former case the onset of instability via a Tanaka-type collision of eigenvalues at zero is identified. The structure of the eigenvalue spectrum is elucidated as the travelling-wave branch is followed revealing a highly intricate structure.

Item Type: Article
Additional Information: Data Availability: The data generated and/or analysed during the current study are available from the corresponding author on reasonable request.
Uncontrolled Keywords: floquet–fourier–hill method,hydroelasticity,linear stability,analysis,modelling and simulation,computational mathematics,applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2603
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Fluid and Solid Mechanics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 05 Dec 2023 02:35
Last Modified: 24 Jan 2024 01:34
URI: https://ueaeprints.uea.ac.uk/id/eprint/93861
DOI: 10.1007/s42286-023-00082-y

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