Multiple resonant scattering of water waves by a two-dimensional array of vertical cylinders: linear aspects.
We study the Bragg resonance of surface water waves by a two-dimensional array of vertical cylinders covering a large area of the sea. Starting from the resonance criterion known in the physics of solid state and crystallography, we employ asymptotic techniques to derive two-dimensional coupled-mode equations for the envelopes of scattered waves resonated by a plane incident wave. Explicit analytical solutions are obtained for a long strip of cylinder array which may be used for supporting a future offshore airport. Examples of both two-wave and three-wave resonances are discussed in detail. Roles of the band gaps are examined.
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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Li
Chiang C
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Mei