Free-surface flow due to a line source near a vertical barrier

Abstract

The unsteady flow generated by a line source that is located at an arbitrary location beneath the free surface of a fluid of finite depth is considered when there is vertical barrier located nearby. The surface may have surface tension. The barrier is shown to have a significant effect on the wave height generated at the barrier and the outward travelling bore generated by the initiation of the flow. Simulations of free surface flows are very difficult due to the formation of curvature singularities on the surface. The method employed in this work does not appear to have these difficulties and the solutions can be computed almost up until the moment the wave breaks, including in some cases a significant spill at the front. A linearized solution and a fully nonlinear solution are presented and the results compared and discussed.