Moving boundary shallow water flow in circular paraboloidal basins

Exact solutions of the nonlinear shallow water wave equations were found by Thacker [1] for frictionless flow involving the Coriolis force in circular paraboloidal basins. The solutions involve a moving shoreline. The motion is oscillatory and continues indefinitely over time. The work in this paper builds on the work of Thacker [1]. As far as the authors of this paper are aware there have been no other analytical solutions of the nonlinear shallow water wave equations as a consequence of the work of Thacker [1]. Holdahl, Holden and Lie [2] and Peterson, Hauser, Thacker and Eppel [3] have compared numerical solutions of the nonlinear shallow water wave equations with some of the analytical solutions in Thacker [1]. In this paper exact solutions of the two dimensional nonlinear shallow water wave equations for flow involving linear bottom friction and without Coriolis force have been found for flow in circular paraboloidal basins. These solutions also involve a moving shoreline. The motion decays over time.