Fluctuation characteristics and topological interface states in the quasi-periodic structures of shallow-water waves

Abstract Compared with periodic structures, quasi-periodic structures have superior band gap properties and topological interface states. In this paper, a one-dimensional quasi-periodic Fibonacci water wave metamaterial model that can be used to apply quasi-periodic structures to shallow-water wave systems is presented. The fluctuation characteristics of periodic and quasi-periodic structures are examined using finite element numerical calculations based on the shallow-water wave equation. The research results show that the band characteristics of quasi-periodic structures are complex, enabling flexible control of the propagation of shallow-water waves. Furthermore, the mirror-symmetrical design of Fibonacci quasi-periodic water wave metamaterials was created to engineer the topological interface states in shallow-water wave systems, ultimately achieving successful localization of wave energy. This research will greatly enrich our understanding of topology, expand the potential applications of quasi-periodic structures, and provide new insights for manipulating water waves and harvesting energy.