On the short cylindrical waves due to a body heaving on water. I

In this paper we obtain the short-wave asymptotic value of the force coefficient for a heaving body partially immersed in the free surface of water which has finite constant depth. The body is required to intersect the free surface normally and have a vertical axis of symmetry. The motion of the water is thus axisymmetric with short outgoing cylindrical waves at a distance, and these must be calculated. For this we use a non-rigorous argument. The potential problem discussed is analogous to the two-dimensional problem afready investigated involving a heaving surface cylinder. Numerical values are obtained in the case of a half-immersed sphere in conclusion.