Modelling rogue waves in 1D wave trains with the JONSWAP spectrum, by means of the High Order Spectral Method and a fully nonlinear numerical model

Probability of rogue wave occurrence due to modulational instability in unidirectional JONSWAP sea states are investigated. This investigation has been conducted based on the quantitative indicators of Benjamin-Feir index (BFI), Π-number and kurtosis, which are used to represent instability in wave trains. Evolution of wavefields is simulated using the fully nonlinear phase-resolving numerical model of Chalikov-Sheinin (CS) and the high order spectral model of HOS-Ocean. Effects of the high-frequency end (tail) of the spectrum on modulational instability and rogue wave evolution are discussed considering four different tail lengths. According to our simulation results, indicators considered for both model results perform as proxy for the occurrence of extreme events. Therefore, it is possible to define a certain interval for the indicators, where the probability of rogue wave occurrence is the highest. Nonlinearity (described in terms of steepness) is the dominant parameter on probability of rogue wave occurrence since it is related to various active physical processes in sea states (both modulational instability and breaking). Rogue wave occurrence increases with increased nonlinearity until it is restricted again by high nonlinearity which causes waves to reach breaking onset earlier. •BFI, Π-number and kurtosis perform as a proxy for the occurrence of extreme events.•Rogue wave occurrence both increases and restricted due to changes in nonlinearity.•Rogue wave modelling are highly dependent on models' ability to simulate breaking.•In highly nonlinear cases, rogue wave probability drops with longer spectral tail.