Modulational instability on nonlinear water waves : experimental study

Abstract

Ocean waves forced by the wind are multi-directional, even if the wind direction is steady. Directionality can occur due to the superposition of long-crested waves propagating at an angle to each other. Lateral modulation of the wave crests, however, also takes place for strictly unidirectional waves, due to nonlinear effects. In this research, the short-crestedness of unidirectional waves is investigated; for this purpose, two experiments on the lateral instability of monochromatic, deep water waves were performed in a large wave basin. In these two tests, long-crested waves were generated with a variety of wave steepnesses, and the emergence and evolution of the modulational instability was quantified and analyzed. The cross-modulation of wave crests was clearly visible, its magnitude depending on the wave steepness in the wave propagation direction and on how many wave cycles the waves travelled. Its spatial scale is comparable with the wavelength. Thus, short-crestedness is an inherent feature of nonlinear waves and should be taken into account when estimating directional properties of ocean waves. The results of the analysis of the set of nonlinear waves generated is presented by quantifying special wave characteristics and parameters related to the modulational instability, namely: 1) the ratio between maximum and minimum amplitude in a single wave crest, 2) the ratio of maximum crest versus mean initial wave crest, and 3) transversal length of the crest modulation were calculated and compared with longitudinal wavelength. It is presented statistics analysis on wave parameters related with nonlinear effects on steep waves, such as wave height and period distributions, and breaking limit and spectral analysis of nonlinear waves.