INVISCID FREE-SURFACE FLOW OVER A PERIODIC WALL

A numerical method is described, based on the hodograph formulation, for analysing inviscid, free-surface flows over a periodic wall. An efficient implementation of the wall boundary condition results in a straightforward method, accurate for a wide range of bottom undulation heights and flow parameters. It is demonstrated that a series of resonances is possible between the bottom undulations and the free surface. The steady, free-surface profiles are accurately calculated for a wide range of current velocities and are shown to be significantly dimpled by higher harmonics. A study of the flow field indicates that the free-surface shape strongly affects the velocities close to the wall, leading to distributions which change dramatically with current velocity. Some implications of the new results on the phenomena of wall dissolution or material deposition, Bragg scattering of surface waves and sediment transport in rivers, are discussed.