Effect of Spectrum Tail Length on Modulational Instability and Freak Wave Occurrence in JONSWAP Sea States

Abstract

Abstract In this study, probability of freak wave occurrence due to modulational instability in JONSWAP sea states are investigated. This investigation has been conducted based on the quantitative indicators of instability in wave spectrum, which are two Benjamin-Feir index (BFI) [1,2] with different spectral bandwidth definitions and Π number [3]. Evolution of wave field are simulated using fully nonlinear phase-resolving Chalikov-Sheinin (CS) numerical model [4,5]. Initial sea surface is controlled with JONSWAP shape parameters (α and γ) and random initial phases. Effect of high frequency end of spectrum on modulational instability and freak wave evolution are discussed by considering 4 different tail lengths. According to simulation results, all parameters that are considered here perform as an indicator for the occurrence of extreme events which makes it possible to define a certain interval for indicators, where freak wave occurrence probability is the highest and potentially dangerous, to be possibly used in extreme wave forecasting. Another key finding is that, modulational instability increases when high frequency part of spectrum is present (longer tail) as expected. Nevertheless, after certain nonlinearity, modulational instability is more prone to result in breaking which significantly decreases the probability of occurrence of freak events. Therefore, spectra with shorter tail length result in more dangerous sea states.