Studying rogue waves using large-scale direct phase-resolved simulations

We investigate the occurrence and dynamics of rogue waves using largescale, three-dimensional, phase-resolved simulations. The direct simulations are based on a high-order spectral method. The method resolves the phases of a large number (up to O(10)) of wave modes, and accounts for nonlinear interactions among them up to an arbitrary high order. Significantly, the simulations obtain exponential convergence, near linear computational effort, and are efficiently implemented on high-performance parallel computers. With this capability we are able to obtain long time (up to O(10) sec) nonlinear evolutions of large (up to O(102∼3) km) phase-resolved three-dimensional wave-fields. Our interest is to use these simulations to obtain the frequency and distribution of rogue wave occurrences and the nonlinear wave-wave interaction, in particular modulation instability, mechanisms underlying the generation and evolution of such rogue waves in open seas. We present the findings from a typical simulation of a nonlinear wave-field generated from JONSWAP spectrum. The occurrence and distribution of rogue waves are analyzed. The local spatial/temporal characteristics of the rogue wave are shown. Energy flux is investigated to explain the formation of rogue waves.