On the resistanceless statement of the two-dimensional Neumann-Kelvin problem for a surface-piercing tandem

A new set of supplementary conditions is proposed for the two-dimensional Neumann-Kelvin problem describing the steady-state forward motion of a surface-piercing tandem in an infinite-depth fluid. This problem is shown to be uniquely solvable for almost every value of the forward speed U. The velocity potential solving the problem corresponds to a flow about the tandem providing no resistance (wave and spray resistance vanish simultaneously). On the other hand, for the exceptional values of U examples of non-uniqueness (trapped modes) are constructed using the inverse procedure recently applied by McIver (J. Fluid Mech. 1996) to the problem of time-harmonic water waves. For the proposed statement of the Neumann-Kelvin problem the inverse method involves the investigation of streamlines generated by two vortices placed in the free surface. The spacing of vortices delivering trapped modes depends on U.