Trapped waves between submerged obstacles

Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. In previous work involving a single obstacle (Dias & Vanden-Broeck 2002), new solutions called 'generalized hydraulic falls' were found. These solutions are characterized by a supercritical flow on one side of the obstacle and a train of waves on the other. However, in the case of a single submerged object, the generalized hydraulic falls are unphysical because the waves do not satisfy the radiation condition. In this paper new solutions for the flow past two obstacles of arbitrary shape are computed. These solutions are characterized by a train of waves 'trapped' between the obstacles. The generalized hydraulic falls are shown to describe locally the flow over one of the two obstacles when the distance between the two obstacles is large.