Rayleigh–Bloch waves above the cutoff

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 wav...

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Bibliographic Details
Published in:Journal of fluid mechanics 2022-06, Vol.940, Article A35
Main Authors: Bennetts, Luke G., Peter, Malte A.
Format: Article
Language:English
Subjects:
Arrays
Bloch waves
Boundary conditions
Cylinders
Damping
Dirichlet problem
Embedding
Helmholtz equations
JFM Papers
Radiation
Wavelengths
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2022.247