Instability growth rates of crossing sea states

Crossing sea states can occur during adverse weather conditions. The instability of such wave trains has been suggested as a possible mechanism for the formation of rogue (freak or extreme) waves. One model for crossing sea states is weakly nonlinear and finite-amplitude short-crested waves (SCWs) on deep water. SCWs are the resonant interaction of two wave systems each with a different direction of propagation. Recently, it has been shown that the stability of these wave interactions is closely associated with the stability of the oblique nonresonant interaction between two waves. The long-wave instability of such waves is considered here; SCWs are used as a benchmark. By using a mismatch of amplitudes, it is demonstrated that instability growth rates of two crossing waves can be larger than those given by SCWs. This indicates that only considering true resonant interactions can underestimate the contribution from unstable crossing sea states to the possible formation of rogue waves.