Numerical study of wave breaking for monochromatic and grouping waves in deep water

A fully nonlinear 2-dimensional numerical wave flume, based on the boundary integral equation method, has been developed. Waves are generated by a hinged paddle wave maker at one end of the flume and a sponge type wave absorber at the other end. A fourth order Taylor expansion technique is used for the time stepping of the free surface. Simple monochromatic waves have been generated and very good agreements are found when compared with Stokes wave profiles. The wave flume is used to study deep water wave breaking due to large periodic displacements of the wave paddle. Wave breaking as a result of energy focusing a group of waves of different frequencies and heights, is also studied. For each breaking event, breaking wave parameters such as the wave steepness, breaking height, particle velocities and accelerations are examined in detail. There does not appear to be a definable correlation between the point of breaking, the wave steepness, or the particle velocities. The maximum downward (vertical) and forward (horizontal) accelerations at breaking are found to be independent of the initial conditions, with constant values of g and 1.56g, respectively; and where g is the acceleration due to gravity. It has been proposed (Philips(1)) that particle accelerations could be used as a criterion for wave breaking. Positive verification of this was first provided in an earlier study by the authors She et al(2), which used spatially periodic boundary conditions. Both studies support Philips' conjecture, and suggest that the point of breaking is when the maximum vertical and horizontal accelerations are at g & 1.56g.