Effect of Real-World Perturbations on Wave Breaking due to a Sharp-Crested Superharmonic Instability

The mechanism for the emergence of breaking water waves in deep water, based on the superharmonic instability of periodic Stokes waves, is tested for the effect of real-world perturbations (dissipation, approximation error, changes in depth, non-zero air density, fluctuations in wave and frame speed). An implicit perturbation is added to a large-amplitude unstable Stokes wave, which is then taken as initial data in a direct numerical solution of the Navier-Stokes equations, using the Basilisk numerical software package. An SVD-based filtering algorithm is used to extract the shape of the unstable wave that grows on the background Stokes wave. We find a dipole shape in the filtered wave that correlates with the superharmonic unstable mode. Our findings show that the inclusion of real-world effects has little qualitative effect, when they are kept small, on the emergence of breaking. We conclude that the mechanism of crest instability of Stokes waves leading to wave breaking is a robust mechanism that is likely to occur in nature.