On the Distributions and Scaling of Energy Flux in Wave Turbulence

While energy cascades in nonlinear dispersive wave systems are widely studied, the properties of these cascades are often in disagreement with the predictions of wave turbulence theory (WTT). We present numerical experiments of a model equation in a two-dimensional periodic domain with fully-resolved steady distributions of forward energy flux P(t) for a range of nonlinear strengths. We compute the contributions to P(t) from four-wave interactions with frequency mismatch |Δω|, yielding a direct measurement of P_q(|Δω|,t), the distribution of P(t) in |Δω|. In regimes of high nonlinearity, our analysis shows that quasi-resonant interactions dominate the mean flux P and drive the large fluctuations present in P(t). We also identify a relationship between P_q(|Δω|,t) and the number of interactions with the same frequency mismatch |Δω|. By using the WTT closure model, we measure P as predicted by the wave kinetic equation (WKE), P_KE. We show that the kinetic scaling of inertial range wave-action N ~ P^1/3 is approximately satisfied even when quasi-resonances are dominant at high nonlinearity levels, however P_KE differs from the true flux P by a factor difference.