ON THE HEAVING MOTION OF A CIRCULAR CYLINDER ON THE SURFACE OF A FLUID

Abstract

We consider the motion of a fluid of infinite depth which arises when a horizontal cylinder of circular cross-section oscillates with small amplitude about a mean position, in which the axis of the cylinder is assumed to lie in the mean surface. It is further assumed that the resulting motion is two-dimensional; this assumption is justified when the cylinder is long compared with a wave-length, or when the fluid is contained between vertical walls at right angles to the axis of the cylinder. Expressions are obtained for the wave motion at a distance from the cylinder, and for the increase in the inertia of the cylinder due to the presence of the fluid.