Statistics of surface gravity wave turbulence in the space and time domains

TL;DR

This study experimentally investigates gravity wave turbulence in a large flume, comparing results with weak turbulence theory and analyzing the coexistence of random and coherent wave structures.

Contribution

It provides the first detailed experimental analysis of surface gravity wave turbulence in space and time, highlighting the roles of random and coherent waves and their impact on spectra and PDFs.

Findings

Wavenumber and frequency spectra depend on wave strength.

Weak turbulence theory aligns with experiments at higher wave intensities.

Random and coherent waves coexist, influencing PDFs and structure functions.

Abstract

We present experimental results on simultaneous space-time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that both wavenumber and the frequency spectra are not universal and dependent on the wave strength, with some evidence in favor of WTT at larger wave intensities when the finite flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (PDF) and the structure functions (SFs). Analyzing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-gaussian PDF core and in the low-order SFs, and the latter - in the PDF tails and the high-order SF's. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than do the t-space SFs. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.