Wave propagation through a gap in a thin vertical wall indeep wáter

Abstract The problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in this paper. It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of th...

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Autores principales:	Das,B. C., De,Soumen, Mandal,B. N.
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2019
Materias:	Thin vertical wall submerged gap integral equations One-term Galerkin approximations Constant as basis Reflection and transmission coefficients.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000300093
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spelling	oai:scielo:S0719-064620190003000932020-02-20Wave propagation through a gap in a thin vertical wall indeep wáterDas,B. C.De,SoumenMandal,B. N. Thin vertical wall submerged gap integral equations One-term Galerkin approximations Constant as basis Reflection and transmission coefficients. Abstract The problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in this paper. It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap. The integral equations are solved approximately using one-term Galerkin approximations involving constants multiplied by appropriate weight functions whose forms are dictated by the physics of the problem. This is in contrast with somewhat complicated but known solutions of corresponding deep water integral equations for the case of normal incidence, used earlier in the literature as one-term Galerkin approximation. Ultimately this leads to very closed (numerically) upper and lower bounds of the reflection and transmission coefficients so that their averages produce fairly accurate numerical estimates for these coefficients. Known numerical results for normal incidence and for a narrow gap obtained by other methods in the literatura are recovered, thereby confirming the correctness of the method employed here.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.21 n.3 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000300093en10.4067/S0719-06462019000300093
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Thin vertical wall submerged gap integral equations One-term Galerkin approximations Constant as basis Reflection and transmission coefficients.
spellingShingle	Thin vertical wall submerged gap integral equations One-term Galerkin approximations Constant as basis Reflection and transmission coefficients. Das,B. C. De,Soumen Mandal,B. N. Wave propagation through a gap in a thin vertical wall indeep wáter
description	Abstract The problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in this paper. It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap. The integral equations are solved approximately using one-term Galerkin approximations involving constants multiplied by appropriate weight functions whose forms are dictated by the physics of the problem. This is in contrast with somewhat complicated but known solutions of corresponding deep water integral equations for the case of normal incidence, used earlier in the literature as one-term Galerkin approximation. Ultimately this leads to very closed (numerically) upper and lower bounds of the reflection and transmission coefficients so that their averages produce fairly accurate numerical estimates for these coefficients. Known numerical results for normal incidence and for a narrow gap obtained by other methods in the literatura are recovered, thereby confirming the correctness of the method employed here.
author	Das,B. C. De,Soumen Mandal,B. N.
author_facet	Das,B. C. De,Soumen Mandal,B. N.
author_sort	Das,B. C.
title	Wave propagation through a gap in a thin vertical wall indeep wáter
title_short	Wave propagation through a gap in a thin vertical wall indeep wáter
title_full	Wave propagation through a gap in a thin vertical wall indeep wáter
title_fullStr	Wave propagation through a gap in a thin vertical wall indeep wáter
title_full_unstemmed	Wave propagation through a gap in a thin vertical wall indeep wáter
title_sort	wave propagation through a gap in a thin vertical wall indeep wáter
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000300093
work_keys_str_mv	AT dasbc wavepropagationthroughagapinathinverticalwallindeepwater AT desoumen wavepropagationthroughagapinathinverticalwallindeepwater AT mandalbn wavepropagationthroughagapinathinverticalwallindeepwater
_version_	1714206804808826880

Wave propagation through a gap in a thin vertical wall indeep wáter

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