  Metamaterials and photonic/phononic crystals have been successfully developed
in recent years to achieve advanced wave manipulation and control, both in
electromagnetism and mechanics. However, the underlying concepts are yet to be
fully applied to the field of fluid dynamics and water waves. Here, we present
an example of the interaction of surface gravity waves with a mechanical
metamaterial, i.e. periodic underwater oscillating resonators. In particular,
we study a device composed by an array of periodic submerged harmonic
oscillators whose objective is to absorb wave energy and dissipate it inside
the fluid in the form of heat. The study is performed using a state of the art
direct numerical simulation of the Navier-Stokes equation in its
two-dimensional form with free boundary and moving bodies. We use a Volume of
Fluid interface technique for tracking the surface and an Immersed Boundary
method for the fluid-structure interaction. We first study the interaction of a
monochromatic wave with a single oscillator and then add up to four resonators
coupled only fluid-mechanically. We study the efficiency of the device in terms
of the total energy dissipation and find that by adding resonators, the
dissipation increases in a non trivial way. As expected, a large energy
attenuation is achieved when the wave and resonators are characterised by
similar frequencies. As the number of resonators is increased, the range of
attenuated frequencies also increases. The concept and results presented herein
are of relevance for applications in coastal protection.
