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ORIGINAL PAPER
Scattering of Oblique Water Waves by an Infinite Step
1
Department of Mathematics, Prasannadeb Women’s College, Jalpaiguri-, 735101, West Bengal, India
2
River Research Institute, West Bengal, Haringhata Central Laboratory, Mohanpur, Nadia, Pin-, 741246, India
Online publication date: 2018-06-04
Publication date: 2018-05-01
International Journal of Applied Mechanics and Engineering 2018;23(2):327-338
KEYWORDS
infinite stepHavelock expansionGalerkin approximationGegenbauer polynomialreflection and transmission coefficients
ABSTRACT
The present paper is concerned with the problem of scattering of obliquely incident surface water wave train passing over a step bottom between the regions of finite and infinite depth. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain very accurate numerical estimates for reflection and transmission coefficients. The numerical results are illustrated in tables.
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