Wave turbulence describes the statistical transfer of energy between interacting waves. The wave period, nonlinear interaction time, phase correlations and resonances determine the transfer rate. A weak wave cascade treats the change in one interaction as small; critical balance instead makes the nonlinear interaction rate comparable to the linear wave frequency.
If a wave packet experiences a fractional nonlinear change per interaction, and successive interaction phases are decorrelated, changes add as a random walk of size . Order-one transfer needs interactions, giving the displayed cascade time. Phase coherence or resonant constraints can alter this estimate; weakness alone does not justify random addition.
