Analytical and numerical prediction of inviscid free surface flow in rotating channel

Starting from two-dimensional Euler's equations in a rotating reference frame, a stream function-based Galerkin finite element method is formulated for inviscid free surface flow in a rotating channel. A new equation governing the free surface is derived to form the Galerkin residual for the free surface. A deforming mesh is used with combined Newton's iteration to solve for the free surface as well as the stream function. Furthermore, an approximate analytical solution is also obtained for the problem. Results show very good agreement between the analytical and numerical solutions, especially when the channel entrance is situated at the axis of rotation.