Numerical recreation of the draupner wave in crossing wave systems using smoothed particle hydrodynamics

Freak waves, abnormally large waves, that occur in the open-ocean can cause significant damage to offshore structures and vessels. In this paper, we attempt to numerically reproduce the experiments of McAllister et al., (2019, J. Fluid Mech. [1]), to investigate the potential properties of the Draupner freak wave [2] in more detail. We use a Smoothed Particle Hydrodynamics (SPH) method to solve the full-3D Navier-Stokes equations. This Lagrangian method is able to recreate wave breaking, and has the potential to fully reproduce these experiments with the aim of providing further insight into properties of the waves created such as their kinematics and geometry. We compare time histories of water surface elevation produced numerically using four different particle sizes with experimentally-obtained data. We find good agreement in the time domain, with r2 (coefficient of determination) values between experimental and numerical data of over 0.94 the error in maximum wave height was less than 5 % for the finest particle size (over 100 million particles). We also numerically reproduce wave breaking observed in the experiments, where jet formation and breaking phenomena are qualitatively similar in appearance.