Nonlinear High Wave Groups in Bimodal Sea States

Abstract

Nonlinear effects for wave groups in bimodal sea states are investigated. The linear free surface displacement is obtained by applying the quasi-determinism theory of the highest waves, with the spectrum given by the superposition of two JONSWAP spectra. Linear groups are modeled as the sum of two groups produced by each unimodal spectrum. Nonlinear effects are given as second-order contribution to the linear free surface displacement. The structure of wave groups is then analyzed for some bimodal spectra. The linear component of wave groups shows a strong variation with respect to the classical structure with unimodal spectra, particularly in mixed seas. It is observed that the nonlinearity gives small contributions for swell dominated seas. For wind dominated sea states, the main nonlinear contribution is given by the wind wave spectral components. For mixed sea states, the interaction among the components of the wind wave spectrum and the components of the swells could give a meaningful contribution to the nonlinear profile. The strongest nonlinear effects occur when the two peaks of the spectrum are close to each other. Finally, the results are validated by means of Monte Carlo simulations of nonlinear sea waves.