Water wave scattering by a thin vertical submerged permeable plate
An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem...
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Vilnius Gediminas Technical University
2021-05-01
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doaj-889e78edabe04dc69339f6421f6d17a22021-07-02T18:58:18ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102021-05-0126210.3846/mma.2021.13207Water wave scattering by a thin vertical submerged permeable plateRupanwita Gayen0Sourav Gupta1Aloknath Chakrabarti2Department of Mathematics, Indian Institute of Technology Kharagpur, 721302 Kharagpur, IndiaDepartment of Mathematics, Indian Institute of Technology Kharagpur, 721302 Kharagpur, IndiaDepartment of Mathematics, Indian Institute of Science, 560012 Bangalore, India An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems. https://journals.vgtu.lt/index.php/MMA/article/view/13207water wave scatteringpermeable plateHavelocks theoremshypersingular integral equationreflection coefficient |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rupanwita Gayen Sourav Gupta Aloknath Chakrabarti |
spellingShingle |
Rupanwita Gayen Sourav Gupta Aloknath Chakrabarti Water wave scattering by a thin vertical submerged permeable plate Mathematical Modelling and Analysis water wave scattering permeable plate Havelocks theorems hypersingular integral equation reflection coefficient |
author_facet |
Rupanwita Gayen Sourav Gupta Aloknath Chakrabarti |
author_sort |
Rupanwita Gayen |
title |
Water wave scattering by a thin vertical submerged permeable plate |
title_short |
Water wave scattering by a thin vertical submerged permeable plate |
title_full |
Water wave scattering by a thin vertical submerged permeable plate |
title_fullStr |
Water wave scattering by a thin vertical submerged permeable plate |
title_full_unstemmed |
Water wave scattering by a thin vertical submerged permeable plate |
title_sort |
water wave scattering by a thin vertical submerged permeable plate |
publisher |
Vilnius Gediminas Technical University |
series |
Mathematical Modelling and Analysis |
issn |
1392-6292 1648-3510 |
publishDate |
2021-05-01 |
description |
An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.
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topic |
water wave scattering permeable plate Havelocks theorems hypersingular integral equation reflection coefficient |
url |
https://journals.vgtu.lt/index.php/MMA/article/view/13207 |
work_keys_str_mv |
AT rupanwitagayen waterwavescatteringbyathinverticalsubmergedpermeableplate AT souravgupta waterwavescatteringbyathinverticalsubmergedpermeableplate AT aloknathchakrabarti waterwavescatteringbyathinverticalsubmergedpermeableplate |
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1721324338709266432 |