Propagation and scattering of waves by dense arrays of impenetrable cylinders in a waveguide |
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| Institution: | 1. School of Naval Architecture and Marine Engineering, National Technical University of Athens, Zografos 15773, Athens, Greece;2. Université de Toulon, Aix Marseille Université, CNRS, IRD, Mediterranean Institute of Oceanography (MIO), La Garde, France;1. Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003, USA;2. Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia;3. Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia;4. Lab of Nonlinear Mathematics and Department of Mechanical Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece;5. Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom;1. Acoustics Division, U.S. Naval Research Laboratory, Stennis Space Ctr., MS 39529, USA;2. Dipartimento di Ingegneria, Università degli Studi di Perugia, 06125 Perugia, Italy;1. Laboratoire Ondes et Milieux Complexes (LOMC) UMR CNRS 6294, Université Le Havre Normandie, France;2. Département de Mathématiques, Université de Lomé, Togo |
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| Abstract: | A coupled numerical scheme, based on modal expansions and boundary integral representations, is developed for treating propagation and scattering by dense arrays of impenetrable cylinders inside a waveguide. Numerical results are presented and discussed concerning reflection and transmission, as well as the wave details both inside and outside the array. The method is applied to water waves propagating over an array of vertical cylinders in constant depth extended all over the water column, operating as a porous breakwater unit in a periodic arrangement (segmented breakwater). Focusing on the reflection and transmission properties, a simplified model is also derived, based on Foldy–Lax theory. The latter provides an equivalent index of refraction of the medium representing the porous structure, modeled as an inclusion in the waveguide. Results obtained by the present fully coupled and approximate models are compared against experimental measurements, collected in wave tank, showing good agreement. The present analysis permits an efficient calculation of the properties of the examined structure, reducing the computational cost and supporting design and optimization studies. |
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| Keywords: | Wave–structure interaction Porous breakwater Modal expansion BEM |
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