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 forextreme wave statistics, the dissipation of wave energy, and air-sea interaction. Numerical methods capableof reliably simulating real-world directionally spread breaking waves are useful for investigating the physicsof wave breaking and for the design of offshore structures and floating bodies. Smoothed Particle Hydrody-namics (SPH) is capable of modelling highly steep and overturning free surfaces, which makes it a promisingmethod for simulating breaking waves. This paper investigates the effect of smoothing length on simulatedwave breaking in both following and crossing seas. To do so, we reproduce numerically the experiments ofhighly directionally spread breaking waves in McAllister et al. [J. Fluid Mech. vol. 860, 2019, pp. 767–786]using a range of normalised smoothing lengths:h/dp=1.4, 1.7, 2.0, 2.3, withhsmoothing length anddpparticle spacing. The smallest smoothing length we use appears to adversely affect the fidelity of thesimulated surface elevation, so that the tallest wave crest observed in experiments is not fully reproduced(coefficient of determinationr2≈0.7). For smoothing lengthsh/dp= 1.7, 2.0, and 2.3, the experiments arewell reproduced (r2≥0.88); in these simulations smoothing length predominantly affects the sp