The Hydrodynamic Forces and Pressure Distributions for an Oscillating Sphere in a Fluid of Finite Depth

摘要

The fluid motion due to a semi-submerged sphere making small vertical oscillations in the free surface of a fluid of finite uniform depth is discussed. The fluid is considered incompressible and non-viscous, and the problem is formulated as a boundary value problem in linear potential theory. The velocity potential is obtained by means of a superposition of a series of singularities, placed within the sphere, in such a manner that all boundary conditions are satisfied. The exact solution contains an infinite series whose coefficients are given by an infinite set of linear simultaneous equations. Since the series converge rapidly, practical computation with a truncated set is possible. In terms of the same expansion coefficients, expressions are also obtained for the hydrodynamic forces as well as the pressure distributions on both the sphere surface and bottom boundary. Numerical calculations of the added mass coefficient, damping parameter and pressure distributions were determined for various fluid depths over a significant frequency range. The results are presented and compared with results of the infinite depth case. The results of the analysis of the influence of the lower boundary at finite depth may be interpreted in terms of the change in surface wavelength, which is a function of the frequency of oscillation and the fluid depth. (Author)