  From among the waves whose dynamics are governed by the nonlinear
Schr\"odinger (NLS) equation, we find a robust, spatiotemporally disordered
family, in which waves initialized with increasing amplitudes, on average, over
long time scales, effectively evolve as ever more weakly coupled collections of
plane waves. In particular, the relative amount of energy contained in their
coupling decays to zero with increasing wave amplitude.
