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ORIGINAL PAPER
Oblique Water Wave Diffraction by a Step
1
Department of Mathematics, Prasannadeb Women's College, Jalpaiguri-735101, West Bengal, India
Online publication date: 2017-03-04
Publication date: 2017-02-01
International Journal of Applied Mechanics and Engineering 2017;22(1):35-47
KEYWORDS
finite stepHavelock expansionGalerkin approximationGegenbauer polynomialreflection and transmission coefficients
ABSTRACT
This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step. 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 ultraspherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for reflection and transmission coefficients which are depicted graphically. From these figures various interesting results are discussed.
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