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

Abstract

The perturbed 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 the weak singular eigen solutions. 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 obtaied in analytical forms. The analytical solution obtained by Bessho-Mizuno(1962) has a possibility that it dose not satisfy the boundary condition on the plate.