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Analysis of linear capillary gravity wave scattering by a submerged plate over an asymmetrical trench

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Názov: Analysis of linear capillary gravity wave scattering by a submerged plate over an asymmetrical trench
Autori: Rumpa Chakraborty, Mampi Majhi
Zdroj: Mathematics in Applied Sciences and Engineering, Vol 6, Iss 2 (2025)
Informácie o vydavateľovi: University of Western Ontario, Western Libraries, 2025.
Rok vydania: 2025
Predmety: T57-57.97, Applied mathematics. Quantitative methods, Water wave scattering, asymmetric trench, surface tension, multi-term Galerkin approximation, orthogonal and simple polynomials, reflection and transmission coefficients
Popis: To protect a harbor from the open sea, one can consider a sustainable construction of breakwater in the form of a submerged vertical thin barrier over an asymmetric rectangular trench. In the present study, the scattering of water waves by submerged vertical breakwater over an asymmetric trench in the presence of capillary gravity wave interaction is considered. Applying linear theory, the scattering problem is investigated in the case of three different positions of a fully submerged barrier in the presence of surface tension. The mathematical problem is structured in terms of integral equations which are operated by using two different numerical approaches, The first one is the Boundary element method and the second one is the multi-term Galerkin Approximation technique where the basis functions are chosen in terms of ultraspherical Gegenbauer polynomials and Chebychev polynomials for the different singularities at the edge of the trench and the barrier respectively. These techniques aid in reducing the integral equation to a system of algebraic equations and they are solved for unknowns. The comparison between the results obtained from the two different techniques is given. Besides, choosing an orthogonal polynomial, one can also choose a simple polynomial as a basis function in Galerkin technique. In the present study, a better convergence rate is given by orthogonal polynomials than simple ones. The effectiveness of the vertical submerged breakwater over an asymmetric trench in the presence of surface tension is studied by analyzing the numerical results for different physical quantities like reflection, transmission coefficients, and wave load which are depicted graphically against wave number. Comparisons between present results and experimental results are shown graphically for reflection and transmission coefficients.
Druh dokumentu: Article
ISSN: 2563-1926
DOI: 10.5206/mase/22320
Prístupová URL adresa: https://doaj.org/article/a6421751a5c645f2b377d3d445832d5a
Rights: CC BY
Prístupové číslo: edsair.doi.dedup.....ec624b5c7a609812c932b697e1053835
Databáza: OpenAIRE
Popis
Abstrakt:To protect a harbor from the open sea, one can consider a sustainable construction of breakwater in the form of a submerged vertical thin barrier over an asymmetric rectangular trench. In the present study, the scattering of water waves by submerged vertical breakwater over an asymmetric trench in the presence of capillary gravity wave interaction is considered. Applying linear theory, the scattering problem is investigated in the case of three different positions of a fully submerged barrier in the presence of surface tension. The mathematical problem is structured in terms of integral equations which are operated by using two different numerical approaches, The first one is the Boundary element method and the second one is the multi-term Galerkin Approximation technique where the basis functions are chosen in terms of ultraspherical Gegenbauer polynomials and Chebychev polynomials for the different singularities at the edge of the trench and the barrier respectively. These techniques aid in reducing the integral equation to a system of algebraic equations and they are solved for unknowns. The comparison between the results obtained from the two different techniques is given. Besides, choosing an orthogonal polynomial, one can also choose a simple polynomial as a basis function in Galerkin technique. In the present study, a better convergence rate is given by orthogonal polynomials than simple ones. The effectiveness of the vertical submerged breakwater over an asymmetric trench in the presence of surface tension is studied by analyzing the numerical results for different physical quantities like reflection, transmission coefficients, and wave load which are depicted graphically against wave number. Comparisons between present results and experimental results are shown graphically for reflection and transmission coefficients.
ISSN:25631926
DOI:10.5206/mase/22320