Trapped modes along a periodic array of freely floating obstacles |
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| Authors: | Gonçalo A S Dias Juha H Videman |
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| Affiliation: | Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal |
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| Abstract: | We consider the coupled problem describing the motion of a linear array of three‐dimensional obstacles floating freely in a homogeneous fluid layer of finite depth. The interaction of time‐harmonic waves with the floating objects is analyzed under the usual assumptions of linear water‐wave theory. Quasi‐periodic boundary conditions and a simplified reduction scheme turn the system into a linear spectral problem for a self‐adjoint operator in Hilbert space. Based upon the operator formulation, we derive a sufficient condition for the nonemptiness of its discrete spectrum. Various examples of obstacles that generate trapped modes are given. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | trapped mode spectral problem freely floating obstacle periodic array |
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