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Article

Bragg Scattering of Surface Gravity Waves Due to Multiple Bottom Undulations and a Semi-Infinite Floating Flexible Structure

1
Department of Statistics, Midnapore College, Midnapore 721101, India
2
Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad 500078, Telangana, India
3
Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
*
Author to whom correspondence should be addressed.
Academic Editors: Mariano Buccino and Alistair Borthwick
Water 2021, 13(17), 2349; https://doi.org/10.3390/w13172349
Received: 7 June 2021 / Revised: 20 August 2021 / Accepted: 20 August 2021 / Published: 27 August 2021
Surface gravity wave interaction with a semi-infinite floating elastic plate in the presence of multiple undulations has been studied under the assumption of linearized water wave theory and small amplitude structural response. The elastic plate is modeled using the Euler-Bernoulli beam equation, whilst the multiple undulations are categorized as an array of submerged trenches or breakwaters. The numerical solution obtained in finite water depth using the boundary element method is validated with the semi-analytic solution obtained under shallow water approximation. Bragg resonance occurs due to the scattering of surface waves by an array of trenches or breakwaters irrespective of the presence of the floating semi-infinite plate. The zero-minima in wave reflection occur when the width of the trench and breakwater is an integer multiple of 0.6 and 0.35 times wavelength, respectively, as the number of trenches or breakwaters increases. In contrast to trenches and breakwaters in isolation, non-zero minima in wave reflection occur in the presence of a semi-infinite plate. Moreover, the number of complete cycles in trenches is less than the number of complete cycles in breakwaters, irrespective of the presence of the floating structure. The frequency of occurrence of zero minimum in wave reflection is reduced in the presence of the semi-infinite plate, and wave reflection increases with an increase in rigidity of the floating plate. Time-dependent simulation of free surface displacement and plate deflection due to multiple undulations of seabed in the presence of the semi-infinite floating plate is demonstrated in different cases. View Full-Text
Keywords: Bragg reflection; trenches; breakwaters; semi-infinite plate; Gaussian wave packet Bragg reflection; trenches; breakwaters; semi-infinite plate; Gaussian wave packet
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MDPI and ACS Style

Kar, P.; Koley, S.; Trivedi, K.; Sahoo, T. Bragg Scattering of Surface Gravity Waves Due to Multiple Bottom Undulations and a Semi-Infinite Floating Flexible Structure. Water 2021, 13, 2349. https://doi.org/10.3390/w13172349

AMA Style

Kar P, Koley S, Trivedi K, Sahoo T. Bragg Scattering of Surface Gravity Waves Due to Multiple Bottom Undulations and a Semi-Infinite Floating Flexible Structure. Water. 2021; 13(17):2349. https://doi.org/10.3390/w13172349

Chicago/Turabian Style

Kar, Prakash, Santanu Koley, Kshma Trivedi, and Trilochan Sahoo. 2021. "Bragg Scattering of Surface Gravity Waves Due to Multiple Bottom Undulations and a Semi-Infinite Floating Flexible Structure" Water 13, no. 17: 2349. https://doi.org/10.3390/w13172349

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