Willis coupling in water waves

Yan Meng,Jensen Li,Shubo Wang,Yiran Hao,Sébastien Guenneau

doi:10.1088/1367-2630/ac0b7d

Abstract

For mechanical waves, Willis coupling means a cross-coupling between stress and velocity or between momentum and strain. In contrary to its realization in acoustic and elastic waves, whether Willis coupling exists in water waves, as another kind of mechanical wave, is still unknown. Here, we propose and establish the concept of Willis coupling in water waves as the cross-coupling between the horizontal velocity at the free surface and the acceleration potential or between the vertical displacement of the water free surface and the flux. Thanks to the surface wave feature of water waves, the proposed metamaterial’s resonating conditions can be tuned by using the wave shoaling effect. With a proper three-dimensional design, Willis coupling can still have significant effects with resonance in the long-wavelength regime. Furthermore, by adding loss in the Willis metamaterial, asymmetric reflectance and absorption can be achieved, which are useful for applications such as seismic isolation, coastal protection, water-wave energy-harnessing, and also for constructing non-Hermitian exceptional points.

Highlights

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not
We numerically demonstrate such a concept is valid in the domain of linear surface water waves, adding a new member for water wave metamaterials with effective constitutive parameters going beyond conventional composites, in addition to already demonstrated negative refraction and negative gravity
The Willis coupling in water waves features a directional dependence of wave propagation, which can be useful for applications such as in seismic isolation, coastal protection, water-wave energy-harnessing, and for constructing non-Hermitian exceptional points

Summary

Introduction

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The metamaterials break the mirror symmetry along y-axis when the rotation angle θ is other than ±90°, and the designed configuration with general θ, will be sufficient to generate significant Willis coupling as a constitutive parameter, with free-space wavelength (inside the background region without resonators) being more than 6 times larger than the size of the unit cell (a) to validate an effective medium picture.

Results

Conclusion