International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 649-661

Shallow water waves in a rotating rectangular basin

Mohamed Atef Helal

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Received 28 July 1999

Copyright © 2000 Mohamed Atef Helal. 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.


This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating rectangular basin. The equations of motion of such a problem with its boundary conditions are reduced to a system of nonlinear equations, which is to be solved by applying the shallow water approximation theory. Each unknown of the problem is expanded asymptotically in terms of the small parameter ϵ which generally depends on some intrinsic quantities of the problem of study. For each order of approximation, the nonlinear system of equations is presented successively. It is worthy to note that such a study has useful applications in the oceanography.