The Analytical Representations for 2-D Flows around a Semi-Submerged Vertical Plate in a Uniform Stream

Abstract

The complex potentials representing flows around a vertical plate semi-submerged in a uniform stream are derived in analytical forms by the reduction method. They are composed from the regular solution and a weak singular eigen solution. The linear combinations of them represent some flows such as regular flow, zero-vertical flux flow, flow satisfying Kutta condition and wave-free flow. The wave resistances of the flows are also obtained in analytical forms. The analytical solution obtained by Bessho-Mizuno(1962) has a possibility that it does not satisfy the boundary condition on the plate.