Role of three-wave interactions in surface gravity wave turbulence

Standard derivation of the Hasselmann kinetic equation for surface gravity waves assumes the dominance of quartet resonant interactions. As a result, the triad-resonance terms are removed from the dynamical equations using a Lee transformation. While such transformation is supposed to be only valid for infinitesimal nonlinearity level, the derived kinetic equation is widely used in wave modeling for finite-amplitude waves. In this work, we numerically study the effect of triad interactions (in particular, the quasi-resonance of three waves) in surface gravity wave turbulence. Our method decomposes the energy transfer into contributions from triad and quartet interactions, thus the role of each type of interaction can be elucidated. We apply this method for both evolving and stationary spectra, and find that the triad interactions play a significant role at low nonlinearity level. The results imply modification of the kinetic equation to better account for the triad interactions in certain cases.