Gayen, R and Gupta, S and Chakrabarti, A (2021) Water wave scattering by a thin vertical submerged permeable plate. In: Mathematical Modelling and Analysis, 26 (2). pp. 223-235.
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Abstract
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. © 2021 The Author(s). Published by Vilnius Gediminas Technical University.
| Item Type: | Journal Article |
|---|---|
| Publication: | Mathematical Modelling and Analysis |
| Publisher: | VGTU |
| Additional Information: | The copyright for this article belongs to Authors |
| Keywords: | Boundary value problems; Surface waters; Water waves, Hypersingular integral; Hypersingular integral equation; Linear water wave theory; Second kinds; Singular integral; Water wave scattering; Wave potentials; Weight functions, Integral equations |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 19 Aug 2021 10:10 |
| Last Modified: | 19 Aug 2021 10:10 |
| URI: | http://eprints.iisc.ac.in/id/eprint/69249 |
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