Control of water waves using time-varying vertical plates

We study theoretically and experimentally the propagation of water waves over a time-varying topography, using thin vertical plates as metamaterials. Starting with the scattering problem of a plane wave incident on a vertical submerged plate inside a water channel, we extract the scattering coefficients as a function of the frequency and the plate height. We then report on harmonic generation, an effect which is observed experimentally when the plate height is a function of time. Finally, we extend the study to the case of a periodic array of plates and investigate both analytically and numerically the two-dimensional propagation of shallow water waves over a time-varying medium, which switches from isotropic to anisotropic at a given time.