... gives[*]
This estimate assumes that if the wave amplitude at some $k$ happened to be of the critical value $s_{nl}$ then it will also be of similar value for a range of $k$'s of width $k$. In other words, strong nonlinearity widens the $k$-space correlation from zero (RPA value) to $k$ (value for the coherent structures involved in the wave breaking). 
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