AN ANALYTICAL SOLUTION FOR OSCILLATIONS WITHIN AN ELLIPTICAL HARBOR

A linear function is obtained by transforming the shallow-water wave equation from rectangular coordinates to elliptic coordinates, which gives the ordinary and the modified Mathieu equations respectively to describe oscillations in the polar and the radial directions by applying the method of separation of variables. Oscillations within an elliptical harbor can be described by appropriate products of radial and angular Mathieu functions. Eigenvalues are obtained by implementing the no-flux condition at the boundary. The oscillation is a two dimension distribution, and there are n nodes running in the polar direction, which is the same as the order of the angular Mathieu function; the nodes in radial direction are related with the boundary condition.