International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 171-177

Reflection of internal waves by sand ripples

Samiran Mandal1 and Uma Basu2

1Khanpara High School, Khari, 24-Parganas (South), India
2Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Calcutta 700009, India

Received 19 July 1992; Revised 13 March 1993

Copyright © 1995 Samiran Mandal and Uma 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.


An investigation is made to study the diffraction of a train of time harmonic progressive waves propagating along the surface of separation of two superposed fluids which are laterally unbounded, the upper fluid being extended infinitely upwards, the lower fluid being of finite depth with sand ripples at the bottom. The first order correction to the velocity potential for the problem of diffraction of interface waves in the presence of bottom deformation is obtained by integral transform technique after introduction of a linear frictional term in the kinematic boundary condition at the surface of separation following Lamb (1932), and the reflection and transmission coefficients are estimated for a patch of sand ripples.