Willis coupling in water waves

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.