Gridless simulations of splashing processes and near-shore bore propagation

The generation and evolution of two-dimensional bores in water of uniform depth and on sloping beaches are simulated through numerical solution of the Euler equations using the Smoothed Particle Hydrodynamics (SPH) method, wherein particles are followed in Lagrangian fashion, avoiding the need for computational grids. In water of uniform depth, a piston wavemaker pro- duces cyclically breaking bores in the Froude number range 1.37 - 1.82, which were shown to move at time averaged speeds in very good agreement with the requirements of global mass and momentum conservation. A single Strouhal number for the breaking period was discovered. Complex repetitive splashing patterns are observed and described, involving forward jet forma- tion growth, impact, and ricochet, and similarly, backward jet formation and impact. Observed consequences were the creation of vortical regions of both signs, dipole creation through pairing, large scale transport of surface water downward, and high tangential scouring velocities on the bed, which are quantified. These bores are further allowed to rise on linear slopes to the shoreline, where they are seen to collapse into a tongue-like flow resembling a dambreak. It is especially to be noted that this essentially inviscid calculation is able to reproduce the development of a highly vortical flow in excellent agreement with experimental observations and theoretical concepts. The turbulent flow behavior is partially described by the numerical solution.