The distribution of wave heights, and therefore the occurrence rate of extreme waves, depends on the shape of the surface elevation spectrum. In an idealized two-layer flow, e.g., fresh water overlaying salt water, the spectral shape of surface waves is modified by class-three triad interactions. We conduct numerical simulations of the wave field evolution on a two-layer stratified fluid. Starting from realistic deep-water JONSWAP spectra, the spectral density at high wavenumbers increases while the variance in the peak region decreases and the peak shifts slightly lower. The enhancement of the spectral tail grows rapidly with increasing initial wave steepness and is strongest for broad-banded spectra. Monte Carlo simulations of surface realizations are performed, where the surface is a linear superposition of wave components taken from the initial and the modified spectra. In all cases, the wave height and crest height distributions can be expressed by modified Rayleigh distributions. On a two-layer flow the probability of rogue waves can be up to two orders of magnitude lower than in the unstratified deep-water case, whereas the probability of rogue crests is nearly unaffected. The average crest-trough correlation, calculated from the spectra, is a good predictor for rogue wave probabilities even for strongly modified spectra with enhanced high-wavenumber spectral variance.

• Received 13 January 2023
• Accepted 21 April 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.054804