A note on the explicit solutions for wave scattering by vertical porous barriers

Manam, S.R.; Sivanesan, M.

doi:10.1016/j.wavemoti.2016.11.010

Cited by 12 publications

(9 citation statements)

References 4 publications

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“…Our present result which is denoted by a solid line matches well with the stars which represent the results of Manam and Sivanesan [19] and this gives another check on correctness of our present analysis.…”

Section: Convergence and Validation Of Resultssupporting

confidence: 90%

“…Employing Green's integral theorem to suitable Green's function and potential function, Gayen and Mondal [12] solved the problem of water wave scattering by vertical and inclined permeable plates by reducing it into a second kind hypersingular integral equation. Manam and Sivanesan [19] developed an analytical method to study the problem of water wave scattering by vertical porous barriers situated in deep water by establishing integral relations between potentials associated with the solid and porous barriers. Sivanesan and Manam [25] obtained analytical solution for the scattering problem involving a porous plate with two gaps by decomposing the associated boundary value problem into four problems involving solid barriers.…”

mentioning

confidence: 99%

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Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

Gayen

Gupta

Chakrabarti

2021

Mathematical Modelling and Analysis

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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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Section: Convergence and Validation Of Resultssupporting

confidence: 90%

mentioning

confidence: 99%

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

Gayen

Gupta

Chakrabarti

2021

Mathematical Modelling and Analysis

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“…The boundary value problem for φ p j (x, y) that is described in the previous section is decomposed into two relatively easy, solvable problems by making use of an integral connection (see the paper by Manam and Sivanesan [10]) as given by…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…At this stage, the involved scattering wave amplitudes R j k , j, k = 1, 2, and R of the decomposed problems are related to R p by (see the paper by Manam and Sivanesan [10])…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…It establishes a connection between the solution potentials that describe wave scattering by a complementary arrangement of partial vertical solid barriers. Moreover, by introducing a modified integral relation between the wave potentials pertaining to scattering problems involving vertical barriers of either a solid or a porous type with a certain configuration, Manam and Sivanesan [10] explicitly solved the scattering problem involving porous barriers.…”

Section: Introductionmentioning

confidence: 99%

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Water Wave Scattering by a Vertical Porous Barrier With Two Gaps

Sivanesan¹,

Manam²

2019

ANZIAM J.

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Explicit solutions are rarely available for water wave scattering problems. An analytical procedure is presented here to solve the boundary value problem associated with wave scattering by a complete vertical porous barrier with two gaps in it. The original problem is decomposed into four problems involving vertical solid barriers. The decomposed problems are solved analytically by using a weakly singular integral equation. Explicit expressions are obtained for the scattering amplitudes and numerical results are presented. The results obtained can be used as a benchmark for other wave scattering problems involving complex geometrical structures.

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Effect of a submerged or a surface piercing porous barrier on structure‐coupled gravity waves

Ashok

Sivanesan

Manam

2023

Math Methods in App Sciences

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Flexural or membrane‐coupled or capillary gravity wave scattering by a submerged or a piercing vertical porous barrier is analytically studied based on a connection that involves the solution potentials and few auxiliary potentials. The problems for the auxiliary potentials are relatively easy to handle for their solutions. The original problem is decomposed into two scattering or radiation problems of this type. The solution wave potential is determined in terms of those resolved wave potentials. Numerical results for the explicitly obtained scattering quantities are also presented.

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A note on the explicit solutions for wave scattering by vertical porous barriers

Cited by 12 publications

References 4 publications

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

Water Wave Scattering by a Vertical Porous Barrier With Two Gaps

Effect of a submerged or a surface piercing porous barrier on structure‐coupled gravity waves

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