Topological water wave state in a one-dimensional structure

TL;DR

This paper introduces the concept of topological phases in a one-dimensional water wave system, demonstrating topological transitions and interface states across different water depths, opening new avenues for water wave management.

Contribution

It is the first study to explore topological properties in water wave systems, revealing topological transitions and interface states in a 1D resonant water tank array.

Findings

Topological transition occurs with varying channel width.

Zak phase characterizes the topological states.

Interface states differ across water depths.

Abstract

Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate its topological transition. By selecting three different water depths, we can construct different types of water waves - shallow, intermediate and deep water waves. The periodic surface-water-wave system consists of an array of cylindrical water tanks connected with narrow water channels. As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase. This topological transition holds true for shallow, intermediate and deep water waves. However, the interface state at the boundary separating two topologically distinct arrays of water tanks can exhibit different bands for shallow, intermediate and deep water waves. Our work studies for the first time topological properties of water wave systems, and paves the way to potential management of water waves.