On the Displacement Potential

Abstract

There exists a displacement potential of which derivative gives approximately a displacement of water particle from the uniform flow in the water motion around a body. In the steady motion, its derivative in the uniform flow direction is proportional to its velocity potential (divided by the uniform velocity) and its vertical one to its stream function in two-dimensional motion and to the Stokes's stream function in three-dimensional axially symmetrical flow. In the oscillatory motion without uniform flow, it is proportional to the velocity potential. Lastly, in the oscillatory motion with a uniform flow, it fascilitates the formulation of the body surface condition, calculations of the velocity potential and hydrodynamical forces.