Modulation Instability and Extreme Events Beyond Initial Three Wave Systems

One possible mechanism that models the dynamics of extreme events in the ocean is the modulation instability (MI). The latter has been discovered in the 60s and significant progress in understanding the physics of modulationally unstable deep-water waves has been achieved since then. The MI instability starts its dynamics from a minor periodic perturbation of a regular Stokes wave, which enhances in amplitude, generating therefore periodic large waves, within the specific range of modulation period. In the spectral domain the same process starts from in amplitude very small symmetric side-band pair, lying in the unstable range from the main carrier frequency peak, which then starts to grow while generating by their own a side-band cascade. We report a new type of periodically modulated and unstable Stokes waves which initial dynamics starts from more that one unique unstable side-band pair. Laboratory experiments have been conducted in a large water wave basin, while numerical simulations have been performed using the modified nonlinear Schrödinger equation and the boundary element method. Both, experiments and numerical simulations are in reasonable agreement. Furthermore, the validity, limitations and applicability of such models will be discussed in detail.