Time-Reversal of Nonlinear Waves - Applicability and Limitations

TL;DR

This paper investigates the effectiveness and limitations of time-reversal techniques in nonlinear water waves through numerical simulations, highlighting the roles of dispersive and nonlinear effects in wave refocusing.

Contribution

It provides a detailed numerical analysis of hydrodynamic time-reversal in nonlinear water waves, expanding understanding of its applicability and limitations in complex media.

Findings

High-order dispersive effects are crucial for accurate wave refocusing.

Nonlinear effects influence the success of time-reversal in stationary solitons.

The approach is effective for certain wave structures but limited by medium complexity.

Abstract

Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.