Numerical Simulation of Collinear Capillary-Wave Turbulence

TL;DR

This paper presents the first numerical evidence of anisotropic capillary-wave turbulence dominated by four-wave interactions, showing a power-law spectrum consistent with theoretical predictions.

Contribution

It demonstrates that four-wave quasi-resonant interactions govern energy transfer in capillary-wave turbulence despite the absence of three-wave resonances.

Findings

Wave spectrum follows a power-law scaling consistent with four-wave turbulence theory.

High-order correlation analysis confirms the dominance of four-wave interactions.

Numerically estimated Kolmogorov-Zakharov spectrum constant.

Abstract

We report on direct numerical simulation of quasi-one-dimensional bidirectional capillary-wave turbulence. Although nontrivial three-wave and four-wave resonant interactions are absent in this peculiar geometry, we show that an energy transfer between scales still occurs concentrated around the linear dispersion relation that is broadened by nonlinearity. The wave spectrum displays a clear wave number power-law scaling that is found to be in good agreement with the dimensionally prediction for capillary-wave turbulence involving four-wave interactions. The carried out high-order correlation analysis (bicoherence and tricoherence) confirms quantitatively the dominant role of four-wave quasi-resonant interactions. The Kolmogorov-Zakharov spectrum constant is also estimated numerically. We interpret our results as the first numerical observation of anisotropic capillary-wave turbulence in which four-wave interactions play a dominant role