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.Comment: 19 pages, 4 figure
