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Type: Journal article
Title: Rayleigh-Bloch waves above the cutoff
Author: Bennetts, L.G.
Peter, M.A.
Citation: Journal of Fluid Mechanics, 2022; 940:A35-1-A35-13
Publisher: Cambridge University Press (CUP)
Issue Date: 2022
ISSN: 0022-1120
Statement of
Luke G. Bennetts, and Malte A. Peter
Abstract: Extensions of Rayleigh–Bloch waves above the cutoff frequency are studied via the discrete spectrum of a transfer operator for a channel containing a single cylinder with quasi-periodic side-wall conditions. Above the cutoff, the Rayleigh–Bloch wavenumber becomes complex valued and an additional wavenumber appears. For small- to intermediate-radius values, the extended Rayleigh–Bloch waves are shown to connect the Neumann and Dirichlet trapped modes before embedding in the continuous spectrum. A homotopy method involving an artificial damping term is proposed to identify the discrete spectrum close to the embedding. Moreover, Rayleigh–Bloch waves vanish beyond some frequency but reappear at higher frequencies for small and large cylinders. The existence and properties of the Rayleigh–Bloch waves are connected with finite-array resonances.
Keywords: surface gravity waves; wave scattering; wave-structure interactions
Rights: © The Author(s), 2022. Published by Cambridge University Press
DOI: 10.1017/jfm.2022.247
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Appears in Collections:Mathematical Sciences publications

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