Rogue wave generation in wind-driven water wave turbulence through multiscale phase-amplitude coupling, phase synchronization, and self-focusing by curved crests

Rogue wave events (RWEs), localized high amplitude extreme events, uncertainly emerge in various nonlinear waves. For RWE generation, modulation instability leading to amplitude soliton formation for one-dimensional (1D) systems; and the additional wave directional property and the ratio of nonlinearity to spectrum bandwidth on the modulation instability for two-dimensional (2D) systems, are the accepted mechanisms. However, those studies have mainly focused on RWEs in weakly disordered wave states dominated by a single scale, but to a much lesser extent on wave turbulence with multiscale excitations. Wind-driven water surface wave turbulence widely occurs in nature. Unraveling RWE generation in wind-driven water surface wave turbulence is an important issue. Here, using multidimensional empirical mode decomposition, we experimentally investigate the dynamics of decomposed multiscale spatiotemporal waveforms of wind-driven water wave turbulence in the 2 + 1D space. We demonstrate how the cascaded amplitude modulation of the faster (higher frequency) modes by the phases of the slower modes, the phase synchronization of the largest peaks in the bursts of fast modes emerging in the crest regions of the medium modes, and self-focusing by the curved crests of the three fastest modes lead to RWE generation.