Prediction of interface states in liquid surface waves with one-dimensional modulation

TL;DR

This paper theoretically investigates how liquid surface waves behave at interfaces created by one-dimensional periodic structures, revealing conditions that lead to localized wave amplification and new ways to control water-wave energy.

Contribution

It introduces a novel theoretical framework for predicting interface states in liquid surface waves using effective parameters derived from periodic structures.

Findings

Effective depth and gravity signs determine interface states.

Interface states can amplify wave amplitudes.

Control of water-wave localization is achieved through structural parameters.

Abstract

We theoretically studied the interface states of liquid surface waves propagating through the heterojunctions formed by a bottom with one-dimensional periodic undulations. Via considering the periodic structure as a homogeneous one, our systematic study shows that the signs of the effective depth and gravitational acceleration are opposite within the band gaps no matter the structure is symmetric or asymmetric. Those effective parameters can be used to predict the interface states which could amplify the amplitudes of liquid surface waves. These phenomena provide new opportunities to control the localization of water-wave energy.