Abstract
The Dirichlet-Neumann operator for the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise, fairly arbitrary) cross-section in a layer of finite depth is constructed in the form of convergent series in powers of the small parameter characterizing the “thinness” of the cylinder. The terms of these series are expressed through the solution of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder. As an application, discrete eigenvalues of this operator which are frequancies of trapped modes of the problem are obtained.
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Acknowledgments
The first and second authors are grateful to CONACYT-M\(\acute{{\text{e}}}\)xico and CIC- UMSNH, and the third author is grateful to Vicerrector\(\acute{{\text{i}}}\)a de Investigaci\(\acute{{\text{o}}}\)n de la UMNG for partial financial support.
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Zhevandrov, P.N., Merzon, A.E. & Romero Rodriguez, M.I. The Dirichlet–Neumann Operator for Oblique Water Waves over a Submerged Thin Cylinder and an Application. Russ. J. Math. Phys. 28, 121–129 (2021). https://doi.org/10.1134/S1061920821010131
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DOI: https://doi.org/10.1134/S1061920821010131