UNIVERSAL ASPECTS OF THE HASSELMANN NONLINEAR-INTERACTION

The asymptotic spectrum of the wave-height autocorrelation is of power-law form for surface gravity waves in deep water. Physical oceanographers have utilized Kolmogorov-type scaling arguments within transport theory in order to predict the exponent of the power law once the wave statistics become stationary. I advance the hypothesis that the asymptotics can be achieved using Hamilton's equations correct to third order with an arbitrary nonsingular interaction term which has the symmetry, degree of homogeneity, and quasilocality in k space of the full Hasselmann interaction term. Examples which support the hypothesis are presented, and its further implications are discussed.