
Simulation of a 2D Vertical Jet by Smoothed Particle Hydrodynamics within an OceanWave3D Wave Field
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Breaking waves are central to energy dissipation and momentum transfer across various fluid systems, including ocean waves, Faraday wave fields, and droplet impacts. Among them, axisymmetric focused waves [1] —characterized by highly focused vertical jets—serve as an idealized yet insightful platform for studying fundamental nonlinear wave dynamics. Despite their rarity in natural settings, these waves uniquely enable the exploration of nonlinear wave theory limits and the mechanisms of its breakdown at extreme curvatures, where pinch-off, droplet ejection, and wave breaking can occur. While significant progress has been made in understanding coastal wave breaking, numerical study of axisymmetric breaking waves remains challenging due to highly localized, complex nonlinear dynamics. We introduce a novel framework coupling the fully nonlinear solver OceanWave3D [2] with the particle-based DualSPHysics [3] in a two-dimensional domain. This approach robustly simulates nonlinear wave energy transfer and vertical jet deformations (Fig. 1b)—phenomena that are difficult to capture with existing models [4]. Figure 1b shows a sharp, cusped wave crest and detailed vertical jet, clearly demonstrating the accurate reproduction of nonlinear energy focusing. Focused waves are generated by superimposing ITTC spectrum frequency components to converge at (x = 0, t = 0). OceanWave3D models these interactions over a 200 m-wide domain, and vertical profiles at x = ±5 m serve as open-boundary conditions for DualSPHysics (Fig. 1a). The coupling method enables us to capture the intricate jet morphology with a high particle resolution (dp = 2 mm). We subsequently use the model to study (a) how local slopes at breaking onset compare to 2D standing-wave theory, (b) dynamic/kinematic criteria for breaking onset detection, and (c) jet height convergence with variable resolution.