The closure problem in a system of random gravity waves

The time behavior of weakly interacting random gravity waves is examined, and equations are derived governing the long‐time behavior of the spectral cumulants. Without any specific statistical assumptions, it is shown that these equations form a closed set, thus rendering the problem theoretically solvable. In particular, the mechanism for energy transfer is found to be primarily due to resonance phenomena. The retraceability of solutions; is discussed in the appendix.