Boundary effects of anisotropic medium on cloaking under shallow-water waves

Abstract

The cloaking of offshore structures exposed to water waves can effectively protect them from hydrodynamics. In this study, an anisotropic medium designed by applying the space transformation method was used to cloak offshore structures exposed to shallow-water waves. By designing a theoretical cloaking space, the wave path could be controlled to bypass a certain area and cloak the structure within the wave field. Based on the form invariance of the shallow-water wave-governing equation, this unique wave path can be physically created using an anisotropic medium that includes water depth and gravity acceleration. First, an anisotropic medium was designed to cloak a single cylinder. The effects of the no-flux inner boundary conditions of the anisotropic medium on cloaking were investigated. The total- and scattered-wave distributions around the structure were calculated and analyzed. The scattering attenuation coefficient was used to measure the cloaking effect. In addition, a numerical truncation method for the medium parameters near the inner boundary was proposed and investigated to analyze the singularity of the medium parameters near the inner boundary. Moreover, an anisotropic medium was introduced to cloak multibody structures in water waves using simplified parameters. The results indicated that the inner area could also be protected without a no-flux boundary. Cloaking was effective in a simplified anisotropic medium. An anisotropic medium with simplified parameters can successfully cloak multibody structures exposed to shallow-water waves.