A boussinesq-type model for waves generated by flow over a bump

A uniform flow disturbed by a bump is studied. The effect of the disturbance is presented at the surface, generating wave. The wave propagation is modeled into a couple of equations, in terms of the surface elevation and the depth average velocity. The numerical solution of the equations is simulated to observe the propagation, especially for long run time, using a predictor-corrector method. A steady solitary surface prole is obtained for supercritical upstream flow, similarly for subcritical flow but for negative amplitude. In the transient process, more waves are generated but some of them propagates to the left or right, and only one wave remains above the bump.