Moving boundary shallow water flow in a region with quadratic bathymetry

Exact solutions of the nonlinear shallow water wave equations for forced flow involving linear bottom friction in a region with quadratic bathymetry have been found. These solutions also involve moving shorelines. The motion decays over time. In the solution of the three simultaneous nonlinear partial differential shallow water wave equations it is assumed that the velocity is a function of time only and along one axis. This assumption reduces the three simultaneous nonlinear partial differential equations to two simultaneous linear ordinary differential equations. The analytical model has been tested against a numerical solution with good agreement between the numerical and analytical solutions. The analytical model is useful for testing the accuracy of a moving boundary shallow water numerical model.