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Rayleigh–Bloch waves above the cutoff

Published online by Cambridge University Press:  12 April 2022

Luke G. Bennetts Open the ORCID record for Luke G. Bennetts [Opens in a new window]  and
Malte A. Peter Open the ORCID record for Malte A. Peter [Opens in a new window]
Luke G. Bennetts*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
Malte A. Peter
Affiliation:
Institute of Mathematics, University of Augsburg, 86135 Augsburg, Germany Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, 86135 Augsburg, Germany
*
†Email address for correspondence: luke.bennetts@adelaide.edu.au
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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.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A35
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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