Analysis of higher harmonics in a focused water wave group by a nonlinear potential flow model

This work analyses the higher harmonic wave elevations of focused wave groups based on the assumption of a Stokes-type nonlinear structure. A fully nonlinear potential flow model is employed to generate nonlinear wave groups by the NewWave theory, which represents an extreme event in a random sea state. We present a methodology to generate high-quality nonlinear wave groups of a narrow-banded wave spectrum in a numerical wave tank. A phase-manipulation approach is employed to accurately extract the higher harmonic elevations. The elevation spectra show clean separation of the first four harmonics. Comparisons with the experimental data show remarkably good agreements for the higher harmonics. We confirm the Stokes-type underlying nonlinear structure of the harmonic elevations in focused wave groups. This is found by simulating wave groups with varying wave steepness and calculating the corresponding elevation coefficients of the higher harmonics. The harmonic coefficients are found almost constant against varying steepness. An implication of the Stokes-type structure for the nonlinear wave elevations is that, it allows us to estimate the higher harmonics based only on the linear component. This is successfully demonstrated by reconstructing a nonlinear focused wave group using the linear NewWave model and the coefficients at its higher harmonics.