Surface gravity wave turbulence: three wave interaction?

We consider the turbulence of potential deep-water surface gravity waves, which have dispersion law Ω k = g k (g is the gravity constant, k=| k | ). It is well known that there are no three wave resonance interaction for such waves, and the lowest-order resonance involves four waves. We show the importance of almost resonance three wave interactions; in particular, they determine the life-span of these waves, provided the range of scales is large enough.