Freely floating structures trapping time-harmonic water waves (revisited)

TL;DR

This paper investigates the existence of axisymmetric floating structures with multiple bodies that can trap time-harmonic water waves, including structures with both moving and motionless bodies, using a generalized semi-inverse method.

Contribution

It introduces a new class of floating structures capable of trapping water waves, extending previous methods to configurations with multiple bodies and mixed motion states.

Findings

Existence of axisymmetric structures trapping water waves

Structures can include both moving and motionless bodies

Construction method based on a generalized semi-inverse procedure

Abstract

We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of $N \geq 2$ bodies; every structure has the following properties: (i) a time-harmonic wave mode is trapped by it; (ii) some of its bodies (may be none) are motionless, whereas the rest of the bodies (may be none) are heaving at the same frequency as water. The construction of these structures is based on a generalization of the semi-inverse procedure applied earlier for obtaining trapping bodies that are motionless although float freely.