Journal
JOURNAL OF FLUID MECHANICS
Volume 940, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2022.247
Keywords
surface gravity waves; wave scattering; wave-structure interactions
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Funding
- Alexander von Humboldt Foundation
- Australian Research Council [FT190100404]
- Australian Research Council [FT190100404] Funding Source: Australian Research Council
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This paper investigates the extensions of Rayleigh-Bloch waves above the cutoff frequency using the discrete spectrum of a transfer operator. The study reveals the complex behavior of Rayleigh-Bloch waves at frequencies above the cutoff, showing connections with the Neumann and Dirichlet trapped modes before embedding in the continuous spectrum. A homotopy method with an artificial damping term is proposed to identify the discrete spectrum close to the embedding. The paper also discusses the disappearance and reappearance of Rayleigh-Bloch waves at different frequencies for small and large cylinders, which is connected to finite-array resonances.
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.
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