Abstract
Phys. Rev. B 101, 014307 (2020) 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.