Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap
In this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite heigh...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2016-05-01
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| Series: | International Journal of Applied Mechanics and Engineering |
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| Online Access: | https://www.ijame-poland.com/Scattering-of-interface-wave-by-bottom-undulations-in-the-presence-of-thin-submerged,167126,0,2.html |
| _version_ | 1797750760565374976 |
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| author | P. Dolai |
| author_facet | P. Dolai |
| author_sort | P. Dolai |
| collection | DOAJ |
| description | In this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green’s integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical wall present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and a suitable application of multi-term Galerkin approximations. The numerical results of the zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature is observed of first-order reflection coefficient due to multiple interactions of the incident wave with bottom undulations, the edges of the submerged wall and the interface. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients. |
| first_indexed | 2024-03-12T16:37:31Z |
| format | Article |
| id | doaj.art-7eea72a6e5a24efca4571d7991742cd3 |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:37:31Z |
| publishDate | 2016-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-7eea72a6e5a24efca4571d7991742cd32023-08-08T14:47:10ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032016-05-0121230332210.1515/ijame-2016-0019167126Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gapP. Dolai0Prasanna Deb Women’s College, Club Road, Jalpaiguri-735 101, West Bengal, INDIAIn this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green’s integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical wall present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and a suitable application of multi-term Galerkin approximations. The numerical results of the zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature is observed of first-order reflection coefficient due to multiple interactions of the incident wave with bottom undulations, the edges of the submerged wall and the interface. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.https://www.ijame-poland.com/Scattering-of-interface-wave-by-bottom-undulations-in-the-presence-of-thin-submerged,167126,0,2.htmlsubmerged vertical wallperturbation analysisinterface wave scatteringsinusoidal bottomgalerkin approximationszero-order reflection coefficientfirst-order reflection coefficient |
| spellingShingle | P. Dolai Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap International Journal of Applied Mechanics and Engineering submerged vertical wall perturbation analysis interface wave scattering sinusoidal bottom galerkin approximations zero-order reflection coefficient first-order reflection coefficient |
| title | Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap |
| title_full | Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap |
| title_fullStr | Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap |
| title_full_unstemmed | Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap |
| title_short | Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap |
| title_sort | scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap |
| topic | submerged vertical wall perturbation analysis interface wave scattering sinusoidal bottom galerkin approximations zero-order reflection coefficient first-order reflection coefficient |
| url | https://www.ijame-poland.com/Scattering-of-interface-wave-by-bottom-undulations-in-the-presence-of-thin-submerged,167126,0,2.html |
| work_keys_str_mv | AT pdolai scatteringofinterfacewavebybottomundulationsinthepresenceofthinsubmergedverticalwallwithagap |