The effects of smoothing length on the onset of wave breaking in smoothed particle hydrodynamics (SPH) simulations of highly directionally spread waves

Ocean wave breaking is a difficult-to-model oceanographic process, which has implications for extreme wave statistics, the dissipation of wave energy, and air–sea interaction. Numerical methods capable of reliably simulating real-world directionally spread breaking waves are useful for investigating the physics of wave breaking and for the design of offshore structures and floating bodies. Smoothed particle hydrodynamics is capable of modelling highly steep and overturning free surfaces, which makes it a promising method for simulating breaking waves. This paper investigates the effect of smoothing length on simulated wave breaking in both following and crossing seas. To do so, we reproduce numerically the experiments of highly directionally spread breaking waves in McAllister et al. (J Fluid Mech 860:767–786, 2019. https://doi.org/10.1017/jfm.2018.886) using a range of normalised smoothing lengths: h/ d_p= 1.4 , 1.7, 2.0, 2.3, with h smoothing length and d_p particle spacing. The smallest smoothing length we use appears to adversely affect the fidelity of the simulated surface elevation, so that the tallest wave crest observed in experiments is not fully reproduced (coefficient of determination r²≈ 0.7). For smoothing lengths h/ d_p= 1.7 , 2.0, and 2.3, the experiments are well reproduced (r²≥ 0.88); in these simulations smoothing length predominantly affects the spatial extent and duration of breaking. Qualitative and quantitative comparison of our simulations shows that values of h/ d_p in the range 1.7 - 2 best reproduce the wave breaking phenomena observed in experiments.