An example of non-uniqueness in the two-dimensional linear water wave problem

M. McIver
1996 Journal of Fluid Mechanics  
An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least
more » ... there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.
doi:10.1017/s0022112096002418 fatcat:uzfnv2bb25g7xdqfkqfzabkirm