Underwater topography invisible for surface waves at given frequencies

Abstract : We consider scattering of surface waves modelled by the linear water wave equation in an unbounded two-dimensional domain of finite depth, at a given frequency and a given incidence. Using asymptotic analysis for small perturbations of the bottom shape, we build a fixed-point equation whose unique solution is a shape which cannot be detected by a distant observer. The method works at any incidence except π/4.
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Submitted on : Monday, February 9, 2015 - 4:31:17 PM
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Anne-Sophie Bonnet-Ben Dhia, Sergei Nazarov, Jari Taskinen. Underwater topography invisible for surface waves at given frequencies. Wave Motion, Elsevier, 2015, 57, ⟨10.1016/j.wavemoti.2015.03.008⟩. ⟨hal-01114632⟩

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