Experimental evidence of nonlinear focusing in standing water waves

TL;DR

This study provides experimental evidence that nonlinear focusing, described by breather solutions of the nonlinear Schrödinger equation, occurs in standing water waves with counter-propagating wave trains, challenging previous assumptions about broadband wave fields.

Contribution

It demonstrates that Peregrine breather-type focusing can occur in standing water waves, even in broadband and directional conditions, supported by experimental data and hydrodynamic modeling.

Findings

Experimental confirmation of PB-type focusing in standing water waves.

Good agreement between measurements and coupled NLSE simulations.

MI can persist in broadband, multi-directional wave fields.

Abstract

Nonlinear wave focusing originating from the universal modulation instability (MI) is responsible for the formation of strong wave localizations on the water surface and in nonlinear wave guides, such as optical Kerr media and plasma. Such extreme wave dynamics can be described by breather solutions of the nonlinear Schr\"odinger equation (NLSE) like by way of example the famed doubly-localized Peregrine breathers (PB), which typify particular cases of MI. On the other hand, it has been suggested that the MI relevance weakens when the wave field becomes broadband or directional. Here, we provide experimental evidence of nonlinear and distinct PB-type focusing in standing water waves describing the scenario of two counter-propagating wave trains. The collected collinear wave measurements are in excellent agreement with the hydrodynamic coupled NLSE (CNLSE) and suggest that MI can undisturbedly prevail during the interplay of several wave systems and emphasize the potential role of exact NLSE solutions in extreme wave formation beyond the formal narrowband and uni-directional limits. Our work may inspire further experimental investigations in various nonlinear wave guides governed by CNLSE frameworks as well as theoretical progress to predict strong wave coherence in directional fields.