In natural conditions, waves are seldom regular, even when produced by almost uniform wind conditions. Instead, a spectrum of amplitudes is generated, which has been repeatedly studied in the literature. Perhaps the most popular model for this spectrum has been published by Hasselmann et al. (1973), after analyzing data collected during the Joint North Sea Wave Observation Project (JONSWAP).
In this video, I show the comparison between regular monochromatic, long-crested waves and stochastic waves produced following the JONSWAP spectrum. In both cases the significant height is 0.9m, with a 4s period. The stochastic waves also include a 5-degree standard deviation in direction.
Notice how the regular waves produce strong interference patterns, which are mostly absent with under stochastic conditions.
Both conditions were computed using the SWASH code, maintained by the Delft University of Technology.