(9)Scattering of water waves by thick rectangular barriers in presence of ice cover
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Anushree Samantaa, Rumpa Chakrabortyb,∗
a Department of Mathematics, Jadavpur University, Kolkata-700032, India
b Department of Mathematics, Diamond Harbour Women’s University, South 24 Parganas-743368, India
Received 24 April 2019; received in revised form 24 January 2020; accepted 25 January 2020
Available online 14 February 2020
Abstract
Assuming linear theory, the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,
is investigated here. Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate. May be the
barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap
presence in water. The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts
of velocity potential function. The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical
Gegenbauer polynomials as its basis function. The numerical solutions of reflection and transmission coefficients are obtained for different
parametric values and these are seen to satisfy the energy identity. These coefficients are depicted graphically against the wave number in a
number of figures. Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments
are also recovered following the present analysis without the presence of ice cover, thereby confirming the correctness of the results presented
here. It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.
© 2020 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Rectangular thick barrier; Ice cover; Water wave scattering; Multi term Galerkin approximation technique; Reflection and transmission coefficients.