Trapped modes and resonances for thin horizontal cylinders in a two-layer fluid
| Autor: | P. Zhevandrov, J.E. De la Paz Méndez, M.I. Romero Rodríguez, Anatoli Merzon |
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| Rok vydání: | 2021 |
| Předmět: |
Laplace's equation
Physics Series (mathematics) Applied Mathematics Mathematical analysis Continuous spectrum General Physics and Astronomy Cylinder (engine) law.invention Physics::Fluid Dynamics Computational Mathematics Flow (mathematics) law Modeling and Simulation Neumann boundary condition Eigenvalues and eigenvectors Convergent series |
| Zdroj: | Wave Motion. 106:102800 |
| ISSN: | 0165-2125 |
| DOI: | 10.1016/j.wavemoti.2021.102800 |
| Popis: | Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are 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. The solutions obtained describe trapped modes corresponding to discrete eigenvalues of the problem (lying close to the cut-off frequency of the continuous spectrum) and resonances lying close to the embedded cut-off. We present certain conditions for the submergence of the cylinder in the upper layer when these resonances convert into previously unobserved embedded trapped modes. |
| Databáze: | OpenAIRE |
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