EXAMPLES OF NONUNIQUENESS FOR THE LINEAR PROBLEM OF POTENTIAL FLOW AROUND SEMI-SUBMERGED BODIES

The plane Neumann-Kelvin problem, which uses a linear approximation of the theory of waves of small amplitude to describe the steady, vortex -free motion of semi-submerged cylindrical bodies in an ideal, incompr essible, heavy liquid with a free surface, is considered. For each fix ed value of the free-stream velocity and a convoy of two or more bodie s it is shown that the geometry of the bodies can be so chosen that th e homogeneous Neumann-Kelvin problem will have a non-trivial solution. A family of potentials is constructed that provide such examples of n on-uniqueness. The corresponding configurations can be obtained by cho osing some of the streamlines of the solutions as the body contours. E xamples are given. (C) 1998 Elsevier Science Ltd. All rights reserved.