Fully-developed Wave Turbulence in the Numerical Kinetic Limit

Wave Turbulence (WT) describes an out-of-equilibrium process in nonlinear wave systems, characterized by inter-scale energy cascades and power-law spectra. Under a few statistical assumptions and in the limits of an infinite domain and small wave amplitude (together, the kinetic limit), a turbulence closure for the evolution of wave action spectrum naturally arises. This closure forms the basis of the widely-adopted weak WT theory. Almost all realistic systems exist outside of the kinetic limit, however, and a quantitative understanding of the WT closure realized in this setting is for the most part lacking.

In this work, we perform a series of high-resolution numerical experiments of fully-developed WT that approximate the kinetic limit. We first compute the full PDFs of instantaneous inter-scale energy flux and dissipation rate. Then, using an interaction-based decomposition of the energy cascade, we quantify the role of resonant interactions in shaping the WT closure. We conclude with a study of stationary spectra and the Kolmogorov constant. At each stage, we draw connections to theoretical predictions.