Guanghua He

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.

Wave concentrators are of significant interest in ocean engineering, as they can greatly enhance the water wave energy density. The protection of the concentrator is essential for its stable operation. A self-protected energy concentrator composed of multiple annularly arranged truncated cylinders has been proposed based on the scattering cancelation method to achieve wave concentration and cloaking effects. In this study, the higher-order boundary element method and wave interaction theory are employed to investigate the hydrodynamic performance of the concentrator. Then, the wave concentration and cloaking effects of the concentrator under various geometric parameter variations are analyzed. Geometric parameter variations of the most downstream cylinder lead to the largest changes in hydrodynamic performance. Furthermore, global geometric parameter variations applied uniformly to all cylinders are found to induce frequency shifts in both the wave concentration and cloaking effects. By adjusting the radial distance of the cylinder array from the concentrator center, synchronous shifts in the wave concentration and cloaking frequencies are successfully achieved, thereby enabling broadband tunability. These results demonstrate a practical approach that exploits geometry-induced scattering interference for simultaneous concentration and cloaking of water waves over a broad frequency band.