Verification of wave turbulence theory in the kinetic limit

Using the 1D Majda-McLaughlin-Tabak model as an example, we develop numerical experiments to study the validity of the wave kinetic equation (WKE) at the kinetic limit (i.e., small nonlinearity and large domain). We show that the dynamics converge to the WKE prediction, in terms of the closure model and energy flux, when the kinetic limit is approached. When the kinetic limit is combined with a process of widening the inertial range, the theoretical Kolmogorov constant can be recovered numerically to a very high precision.