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

TL;DR

This paper derives analytical complex potential solutions for 2-D flows around a semi-submerged vertical plate in a uniform stream, including various flow types and wave resistance, improving understanding of flow behaviors around such structures.

Contribution

It presents new analytical representations of flow around a semi-submerged vertical plate, incorporating solutions that satisfy different boundary conditions and calculating wave resistance explicitly.

Findings

Derived analytical complex potentials for multiple flow types.

Obtained explicit formulas for wave resistance.

Identified limitations of previous solutions like Bessho-Mizuno(1962).

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.