Near Shore Bore Propagation and Splashing Processes: Gridless Simulations

Great advances have taken place in the simulation of water wave propagation by boundary element methods up through the formation of a plunging breaker, both in deep water (Wang, et al 1995) and in a shallow water and on beaches (Grilli, et al 1997). However, it has been apparent for some time that new numerical approaches are necessary if we are to gain understanding and to simulate processes in water waves after the jet splashes down, throughout the post-breaking phase in the case of deep water waves, and continually throughout the cyclical splashing phase characteristic of bores, for instance. The existence of an appropriate numerical approach would immediately surmount the problems which theories have long had to predict the behaviour of highly non-linear flows like bores on beaches, or high amplitude sloshing in containers, or bow waves on ships, using highly idealized mathematical methods. In fact, it is only after seeing the enormously complicated behaviour of the free surface in producing ricochets, backward facing jets, folded shapes, holes, and vortical structures, that a true appreciation of the hydrodynamic complexities can be realized. In order to be able to simulate the post breaking behaviour of waves around ships and in their wakes, we had proposed at the OEL-UCSB the evolution of an existing gridless, Lagrangian method (SPH), which is well grounded mathematically, and we have subsequently formed an international team to carry out this development and its application, centered at the OEL.