International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 363-370
doi:10.1155/S0161171296000506
Oblique interface-wave diffraction by a small bottom deformation in two superposed fluids
1Physical and Earth Sciences Division, Indian Statistical Institute 203, Barrackpore Trunk Road, Calcutta 700035, India
2Department of Applied Mathematics, University of Calcutta 92, APC Road, Calcutta 700009, India
; Revised 12 December 1994
Copyright © 1996 B. N. Mandal and U. Basu. 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 problem of diffraction of oblique interface-waves by a small bottom
deformation of the lower fluid in two superposed fluids has been investigated here assuming linear theory
and invoking a simplified perturbation analysis. First order corrections to the velocity potentials in the
two fluids are obtained by using the Green's integral theorem in a suitable manner. The transmission and
reflection coefficients are evaluated approximately. These reduce to the known results for a single fluid
in the absence of the upper fluid.