Discussion --

In this manuscript, we derived a hierarchy of equations (10) for the one-point moments $M^{(p)}_k$ of the waveaction $\vert a_k\vert^2$. This system of equations has a ``triangular'' structure: the time derivative of the $p$-th moment depends only on the moments of order $p, p-1$ and 1 (spectrum). Their evolution is not ``slaved'' to the spectrum or any other low moments and it depends on the initial conditions. RPA allows the initial conditions to be far from Gaussian and deviation of n'th moment from its Gaussian level may even increase in a transient time dependent state. Among two allowed extreme limits are the wavefield with a deterministic amplitude $\vert a_k\vert$ (for which $M^{(p)}_k = n^p_k$) and the intermittent wavefields characterized by sparse k-space distributions of $\vert a_k\vert$ (for which $M^{(p)}_k \gg n^p_k$). However, the level of intermittency (and non-Gaussianity in general) exponentially decreases as WT approaches a statistically steady state, as given by (13). Importantly, in some situations WT might never reach a steady state (for example because of the nonstationary pumping) or it might spend a long time in a transient non-stationary state. In this case WT can be highly intermittent and yet equations (10) are still valid for description of such turbulence. In the other words, the type of intermittency discussed in the present manuscript appears within the weakly nonlinear closure and not as a result of its breakdown as in [10]).

Acknowledgments Authors thank anonymous referees for constructive comments and Alan Newell for enlightening discussions. YL is supported by NSF CAREER grant DMS 0134955 and by ONR YIP grant N000140210528. SN thanks ONR for the support of his visit to RPI.