Nonlinear evolution of wind waves during the transition phase and their interaction with swell at dual crossing angles

The characteristics of wind waves at the transition stage are investigated, and their interaction with the following and opposing swell is comparatively studied with spectral and statistical methods. Wind forcing induces a rapid increase in crest height, while the wavelength growth lags behind the amplitude development. Therefore, the higher wind waves, composed of shallower troughs, cannot be maintained after leaving the fetch region, significantly reducing the chance of generating an abnormal wave. Encountering heavy swell, the peak energy of wind waves tends to be attenuated, with its location shifted to a lower band. Although the nonlinear energy exchange among low-frequency components is more dramatic in the counter-propagating system, the tail slope in the saturation range of wind wave spectra is primarily determined by the type of swell, insensitive to crossing angle and wind speed. An exponential decay rate is identified for the relative energy variation of swell, which tends to be unstable in space in the co-propagating systems. Colliding with wind waves can always enhance swell energy growth and trigger higher-order bound wave components. Higher crests are generated in counter-propagating waves, while deeper troughs are formed in co-propagating waves. Consequently, larger waves derived at these two crossing angles are comparable in height but distinctly different in crest-trough asymmetry. Moreover, the bimodal distributions of crest heights and trough depths, only detected in the counter-propagating waves, can eventually evolve into a unimodal one, after the complex nonlinear wind wave and swell interaction.