Control of water waves by time-varying metamaterials

The control of water waves using time-varying metamaterials is investigated. These metamaterials consist of vertical, infinitesimally thin, rigid plates placed on the fluid bottom, with time-dependent height. First, we focus on a single vertically oscillating plate placed perpendicularly to the direction of propagation in a water channel. The scattering problem of a monochromatic wave incident on the oscillating plate is solved in the shallow water limit, yielding the generation of harmonics around the fundamental frequency. Then, the stability of the free water surface with respect to the plate oscillation is characterized inside a closed cavity, revealing parametric amplification windows. Finally, a plate array with the property to descend abruptly at the fluid bottom is used in order to deflect a wavepacket in shallow water. The plate array creates an effective anisotropic medium, which modifies the direction of the group velocity vector compared to a plate-free domain. By removing the plate array, the medium is switched to isotropic and the wavepacket is redirected. This mechanism, combining anisotropy and temporal interface to deflect wavepackets and known as temporal aiming, is demonstrated experimentally using space–time resolved measurements.