International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 649-661
doi:10.1155/S0161171200004932
Shallow water waves in a rotating rectangular basin
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.
Abstract
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.