The Impact of the Spectral Tail on the Kurtosis of Random Seas

Abstract We perform Modified Nonlinear Schrödinger (MNLS) simulations of random seas based on narrow-banded JONSWAP spectra (γ = 6) with directional spreading. Our wavefields are homogeneous in space and non-stationary in time, initialised with Gaussian statistics. We truncate the spectral tail for the initial conditions at different cut-off wavenumbers to assess the impact of the spectral tail on the kurtosis and spectral evolution. We consider two distinct cases based on truncation of the wavenumber tail at |k|/kp = 2.4 and |k|/kp = 6, where kp is the wavenumber of the spectral peak. A comparison of our results with previous experiments and simulations yields good agreement, supporting the findings of our study. Our simulations indicate that the peak kurtosis value increases if the tail is truncated at |k|/kp = 2.4 rather than |k|/kp = 6. For the case with a wavenumber cut-off at |k|/kp = 2.4, augmented kurtosis is accompanied by comparatively more aggressive spectral changes including redevelopment of the spectral tail, rapid broadening of the spectrum and downshifting of the spectral peak. Similar trends are observed for the case with a wavenumber cut-off at |k|/kp = 6, but the spectral changes are less rapid and less substantial. Thus, the spectral tail appears to play an important role in a form of spectral equilibrium that reduces spectral changes and decreases the peak kurtosis value. Our findings suggest that care should be taken when truncating the spectral tail for the purpose of simulations/experiments. We also find that the kurtosis evolution equation of Fedele (2015, J. Fluid Mech., vol. 782, pp. 25–36) provides an excellent estimate of the peak kurtosis value. However, the selected bandwidth parameter must account for the spectral tail to provide accurate estimates of the peak kurtosis.