Scattering theory and cancellation of gravity-flexural waves of floating plates

TL;DR

This paper develops a combined scattering theory for water and flexural waves in floating plates, enabling control of wave scattering with potential applications in ocean wave manipulation.

Contribution

It introduces a novel approach combining water wave and flexural wave theories to analyze and control wave scattering using floating plates.

Findings

Scattering dominated by zeroth-order multipole in gravity-flexural waves.

Non-vanishing scattering cross-section at zero frequency.

Reduction of the problem to a linear algebraic system.

Abstract

We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential equation with appropriate boundary conditions of the velocity potential. Making use of multipole expansions, we reduce the scattering problem to a linear algebraic system. The response of a floating plate in the quasistatic limit simplifies, considering a distinct behavior for water and flexural waves. Unlike similar studies in electromagnetics and acoustics, scattering of gravity-flexural waves is dominated by the zeroth-order multipole term and this results in non-vanishing scattering cross-section also in the zero-frequency limit. Potential applications lie in floating structures manipulating ocean waves.