Freak waves in crossing seas

We consider the modulational instability in crossing seas as a potential mechanism for the formation of freak waves. The problem is discussed in terms of a system of two coupled Nonlinear Schröedinger equations. The asymptotic validity of such system is discussed. For some specific angles between the two wave trains, the equations reduce to an integrable system. A stability analysis of these equations is discussed. Furthermore, we present an analytical study of the maximum amplification factor for an unstable plane wave solution. Results indicate that angles between 10° and 30° are the most probable for establishing a freak wave sea. We show that the theoretical expectations are consistent with numerical simulations of the Euler equations.