Chakrabarti, A (2000) On the solution of the problem of scattering of surfacewater waves by the edge of an ice cover. In: Proceedings of the Royal Society of London Series A Mathematical Physical and Engineering Sciences, 456 (1997). pp. 10871099.

PDF
solution.pdf Download (213kB) 
Abstract
The mixed boundaryvalue problem arising in the study of scattering of twodimensional timeharmonic surfacewater waves by a discontinuity on the surface boundary conditions, separating the clean surface and an icecovered surface, is solved completely in the case of an infinite depth of water. The main problem is reduced to that of solving a singular integral equation, of the Carleman type, over a semifinite range and the explicit solution of the original problem is determined. Neat and computable expressions are derived for the two most important quantities, known as the reflection and transmission coefficients, occurring in such scattering problems and tables of numerical values of these quantities are presented for specific choices of a parameter modelling the ice cover. The absolute values of the reflection and transmission coefficients are presented graphically. The present method of solution of the boundaryvalue problem produces simple expressions far the principal unknowns of the problem at hand and thus provides an easily understandable alternative to the rather complicated WienerHopf method used previously.
Item Type:  Journal Article 

Publication:  Proceedings of the Royal Society of London Series A Mathematical Physical and Engineering Sciences 
Publisher:  Royal Society London 
Additional Information:  Copyright for this article belongs to Royal Society London. 
Keywords:  scattering;surfacewater waves;ice cover;Fourier analysis;Carlemantype singular integral equations;RiemannHilbert problem 
Department/Centre:  Division of Physical & Mathematical Sciences > Mathematics 
Date Deposited:  08 Nov 2004 
Last Modified:  19 Sep 2010 04:15 
URI:  http://eprints.iisc.ac.in/id/eprint/1714 
Actions (login required)
View Item 