Shallow water waves in a rotating rectangular basin

This paper is mainly concerned with the motion of an incompressiblefluid in a slowly rotating rectangular basin. The equations ofmotion of such a problem with its boundary conditions are reducedto a system of nonlinear equations, which is to be solved byapplying the shallow water approximation theory. Each unknown ofthe problem is expanded asymptotically in terms of the smallparameter ϵ which generally depends on some intrinsicquantities of the problem of study. For each order ofapproximation, the nonlinear system of equations is presentedsuccessively. It is worthy to note that such a study has usefulapplications in the oceanography.