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MEMBRANE-COUPLED GRAVITY WAVE SCATTERING BY A VERTICAL BARRIER WITH A GAP

Part of: Systems of linear integral equations Waves

Published online by Cambridge University Press:  05 June 2014

S. R. MANAM  and
R. B. KALIGATLA
S. R. MANAM*
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India email manam@iitm.ac.in
R. B. KALIGATLA
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India email manam@iitm.ac.in
*
✉manam@iitm.ac.in
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Abstract

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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.

Keywords

mixed boundary value problemmode-coupling relationsingular integral equationmembrane and surface tensionreflection coefficient

MSC classification

Secondary: 74J20: Wave scattering 45F10: Dual, triple, etc., integral and series equations
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 3 , January 2014 , pp. 267 - 288
Copyright
Copyright © 2014 Australian Mathematical Society 

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