The Decay of the Free Motion of a Floating Body

Abstract

We consider the time-domain problem of a floating half-immersed horizontal circular cylinder of radius a. This is the simplest and best studied problem in the interaction of water waves and floating bodies. The motion of the body is constrained to heave only, subject to the linear equations of water waves and body motion. Viscosity and surface tension are neglected. While this problem has been well studied, there are still unanswered questions about the large time behaviour of the system and this is the principal focus of our investigation. Because of the simple geometry of the body, we are able to use multipole expansions to solve for the displacements of the body in the frequency domain. We then use a generalized eigenfunction solution, which has been recently developed, in which the time-domain problem can be solved using the frequency domain solutions. We present numerical results for the heaving cylinder, and compare our results with previous results.