On a cylinder freely floating in oblique waves

TL;DR

This paper analyzes the coupled motion of a floating cylinder and water in oblique waves, establishing spectral properties and energy distribution, and proving the absence of trapped wave modes under certain conditions.

Contribution

It introduces a spectral framework for the coupled water-body system in oblique waves and proves the non-existence of trapped modes for specific frequency ranges.

Findings

Total energy is finite with energy equipartition in the system.

No trapped wave modes exist under certain frequency restrictions.

Spectral problem formulation for small amplitude, time-harmonic oscillations.

Abstract

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study the so-called oblique waves. Under the assumption that the motion is of small amplitude near equilibrium and describes time-harmonic oscillations, the phenomenon's linear setting reduces to a spectral problem with the radian frequency as the spectral parameter. If the radiation condition holds, then the total energy is finite and the equipartition of kinetic and potential energy holds for the whole system. On this basis, it is proved that no wave modes are trapped under some restrictions on their frequencies; in the case when a symmetric cylinder has two immersed parts restrictions are imposed on the type of mode as well.