Deep water wave cloaking using a multi-layered buoyant plate

Trajectory of surface gravity waves in potential flow regime is affected by the gravitational acceleration, water density, and seabed depth. While the gravitational acceleration and water density are approximately constant, the effect of water depth on surface gravity waves exponentially decreases as the water depth increases. In shallow water, cloaking an object from surface waves by varying the seabed topography is possible, however, as the water depth increases, cloaking becomes a challenge since there is no physical parameter to be engineered and subsequently affects the wave propagation. In order to create an omnidirectional cylindrical cloaking device for finite-depth/deep-water waves, we propose a multi-layered elastic plate that floats on the surface around a to-be-cloaked cylinder. The buoyant elastic plate is made of axisymmetric, homogeneous, and isotropic layers which provides adjustable degrees of freedom to engineer and affect the wave propagation. We first develop a pseudo-spectral method to efficiently determine the wave solution for a multi-layered buoyant plate. Next, we optimize the physical parameters of the buoyant plate (i.e. elasticity and mass of every layer) using a real-coded evolutionary algorithm to minimize the energy of scattered-waves from the object. We show that the optimized cloak reduces the energy of scattered-waves as high as 99.2% for the target wave number. We also quantify the wave drift force exerted on the structures and show that the buoyant plate reduces the exerted force by 99.9%.