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. © 2019 Australian Mathematical SocietyA.

Srinivasa Rao Manam

Department of Mathematics

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IIT Madras

ANZIAM Journal

Complete analytical solutions are obtained here for normally incident water wave scattering by vertical porous barriers of various configurations. By allowing incident waves from either direction separately, two quarter-plane problems are posed for porous potentials associated with the physical problem as well as for solid potentials associated with the scattering problem that involves the vertical solid barrier of same configuration. Then, two integral relations are introduced to establish a link between the porous and the solid wave potentials. They involve auxiliary wave potentials that describe radiation of bi-directional waves by the solid barrier. Moreover, they aid to decompose the original problem into four analytically solvable problems in a quarter-plane and to determine the porous potentials explicitly. © 2016 Elsevier B.V.

Wave Motion

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

An analytical approach is proposed here to study scattering of deep water waves by a submerged or a surface piercing vertical porous barrier. It involves a connection between two wave potentials of which one is the solution of a boundary value problem associated with wave scattering by the porous barrier and the other is the solution of a complementary type problem where barrier and gap positions are interchanged and solid barrier takes the position of the porous barrier. The connection also involves an auxiliary or a connection wave potential. The potential for the solid barrier problem involves incident wave forcing while the auxiliary potential describes a solid barrier type problem that involves a non-physical forcing. The solution procedure of Ursell (Ursell, 1947) is chosen to solve these boundary value problems explicitly in the case of normal wave incidence as it also determines necessary exact behavior of the potential at the barrier edge. The reflection coefficients are also connected and the reflection amplitudes of the normally incident wave against the vertical porous barriers are obtained analytically. Numerical results for reflection and transmission coefficients are presented. © 2016 Elsevier B.V.

Scattering of water waves by vertical porous barriers: An analytical approach

We study the reflection of membrane-coupled gravity waves in deep water against a vertical barrier with a gap. A floating membrane is attached on both sides of the barrier. The associated mixed boundary value problem, which is not particularly well posed, is analysed. We utilize an orthogonal mode-coupling relation to reduce the problem to solving a set of dual integral equations with trigonometric kernel. We solve these by using a weakly singular integral equation. The reflection coefficient is determined explicitly, while having freedom to clamp the membrane with a spring of a certain stiffness on only one side of the vertical barrier. The physical problem is of capillary-gravity wave scattering by a vertical barrier with a gap, when the membrane density is neglected. In this case, the reflection coefficient is known up to an undetermined edge slope on either side of the barrier. The scattering quantity is computed and presented graphically against a wave parameter for different values of nondimensional parameters pertaining to the structures involved in the problem. © 2014 Australian Mathematical Society.

Journal	Data powered by TypesetANZIAM Journal
Publisher	Data powered by TypesetCambridge University Press
ISSN	14461811
Open Access	No