Finite-system size effects in gravity-capillary wave turbulence

TL;DR

This study experimentally explores how finite-system size influences gravity-capillary wave turbulence, revealing a transition from discrete to continuous turbulence and the impact on wave interactions.

Contribution

It provides new insights into finite-size effects on wave turbulence, demonstrating tunable spectral properties and the transition between different turbulence regimes.

Findings

Finite-size effects modify wave energy spectra and mode structures.

A smooth transition from discrete to continuous turbulence is observed.

Finite size alters wave interaction dynamics, especially three-wave resonances.

Abstract

We experimentally investigate the effects of finite-system size on the dynamics of weakly nonlinear random gravity-capillary surface waves. Experiments are conducted in rectangular tanks with varying aspect ratios, in which the fluid surface is perturbed locally and erratically by small, partially submerged magnets. Driven by an oscillating vertical electromagnetic field, these magnets generate a statistically homogeneous and isotropic random wave field. This setup enables us to probe finite-size effects without the dominant influence of global forcing present in horizontally oscillated tanks. Spatiotemporal measurements of the wave field reveal multiple branches in the wave-energy spectrum along the unconfined direction, corresponding to sloshing modes in the confined direction. We show that the spectral properties of these modes can be tuned by varying either the wave steepness or the confinement. Signatures of discrete wave turbulence in the confined direction and mesoscopic continuous wave turbulence in the unconfined direction are observed. As the confinement is gradually relaxed, we further demonstrate a smooth transition from discrete to continuous wave turbulence, consistent with the nonlinear-to-discreteness timescale ratio. Using high-order correlation analysis, we also show that finite-size effects alter wave dynamics by depleting two-dimensional three-wave resonant interactions along the confined direction.