Characterisation of temporal aiming for water waves with an anisotropic metabathymetry

TL;DR

This paper investigates the phenomenon of temporal aiming in water waves through a time-varying anisotropic metabathymetry, combining modeling, numerical simulations, and experimental validation to demonstrate wavepacket deflection caused by rapid medium changes.

Contribution

It introduces the concept of temporal aiming for water waves using a dynamic anisotropic bathymetry and provides a comprehensive analysis including theory, simulations, and experiments.

Findings

Wavepacket deflection due to rapid medium change

Quantitative scattering coefficients and deviation angles

Experimental confirmation of trajectory shift

Abstract

The deflection of waves by combining the effects of time modulation with anisotropy has been recently proposed in the context of electromagnetism. In this work, we characterise this phenomenon, called temporal aiming, for water waves using a time-varying metabathymetry. This metabathymetry is composed of thin vertical plates that are periodically arranged at the fluid bottom and which act as an effective anisotropic medium for the surface wave in the long-wavelength approximation. When this plate array is vertically lifted at the fluid bottom at a given time, the medium switches from isotropic to anisotropic, causing a wavepacket to scatter in time and deflect from its initial trajectory. Following a simple modelling, we obtain the scattering coefficients of the two waves generated due to the sudden medium change as well as the angle of deviation with respect to the incident angle. We then numerically evaluate this scattering problem with simulations of the full 2D effective anisotropic wave equation, with a time-dependent anisotropy tensor. Finally, we provide experimental evidence of the temporal aiming, using space time resolved measurement techniques, demonstrating the trajectory shift of a wavepacket and measuring its angle of deviation.