Weak Cloaking in Water Waves via Spatial-Transformation Metamaterials

When water waves encounter marine structures, significant scattering is produced, which affects the stability and safety of marine equipment. The cloaking of marine structures in water waves, achieved by water-wave transformation metamaterials, provides a new approach to solving this problem. However, in the anisotropic water depth required for perfect cloaking, the radial water depth tends to infinity, and the circumferential water depth tends to zero at the edge of the structure, leading to a singularity problem. This results in extreme parameters of the metamaterial near the structure, making fabrication difficult. To address the above issue, a comb-type metamaterial for weak scattering of water waves is designed in this paper based on space-transformation metamaterials, by which optimized control over the scattering characteristics of water waves is achieved. First, a general nonlinear spatial transformation is designed for both weak scattering and perfect cloaking. Then, the anisotropic water depths and equivalent gravitational acceleration parameters for the two cases are calculated and analyzed. Subsequently, the Helmholtz equation is solved using the finite element method, and the distributions of wave fields under anisotropic water depths and metamaterials for weak scattering and perfect cloaking are compared and analyzed. The results show that for weak scattering, the radial and circumferential water depths tend to constant values at the edge of the structure, thus resolving the singularity problem in perfect cloaking, while the control performance over water waves is comparable. Compared with perfect-cloaking metamaterials, the designed weak-scattering metamaterial significantly reduces the water depth parameters near the structure while maintaining water-wave control performance, making it easier to fabricate.