Table of Contents
ISRN Oceanography
Volume 2013, Article ID 504879, 6 pages
http://dx.doi.org/10.5402/2013/504879
Research Article

Wave Scattering by Small Undulation on the Porous Bottom of an Ocean in the Presence of Surface Tension

1Department of Mathematics, Indian Institute of Technology Ropar, Nangal Road, Rupnagar 140 001, India
2Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar 751 004, India

Received 30 April 2012; Accepted 26 June 2012

Academic Editors: C. Grenz and J. L. Zhou

Copyright © 2013 Srikumar Panda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The scattering of incident surface water waves due to small bottom undulation on the porous bed of a laterally unbounded ocean in the presence of surface tension at the free surface is investigated within the framework of two-dimensional linearized water wave theory. Perturbation analysis in conjunction with the Fourier transform technique is employed to derive the first-order reflection and transmission coefficients in terms of integrals involving the shape function ๐‘(๐‘ฅ) representing the bottom undulation. One special type of bottom topography is considered as an example and the related coefficients are determined in detail. These coefficients are presented in graphical forms. The theoretical observations are validated computationally. The results for the problem involving scattering of water waves by bottom deformations on an impermeable ocean bed are obtained as a particular case.