Direct Numerical Simulation of the First Stages of a Plunging Breaker Using a Level Set Method

Abstract

A numerical study of wave breaking in shallow water is presented. The jet formed at the wave crest and the subsequent splash-up phenomenon resulting from the impact of the jet on the liquid surface are analyzed. The wave is assumed to be generated by an accelerated piston in an open channel containing liquid. The two-dimensional, incompressible, unsteady Navier-Stokes equations are solved using a local level set method to treat the interface evolution [Go´mez et al., Int. J. Numer. Meth. Engng, 63, pp. 1478–1512, 2005], which permits to analyze the combined air-liquid flow. Viscous and capillary effects are retained. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid. Two different approaches are considered to take into account the relative movement between the piston and the end wall of the channel. The first one uses a fixed grid and introduces a mass force per unit mass equal to the piston acceleration, and the second one is based on using a moving grid, which is compressed as the piston moves forward, and an arbitrary Lagrangian-Eulerian method. The numerical results obtained for the evolution of the wave shape during the breaking process, particularly the evolution of the plunging jet, the air cavity and the complex flow resulting from the impact of the plunging jet, are compared with experimental visualization results obtained for a small-scale breaking wave, for which the breaking process is strongly influenced by surface tension. A good degree of agreement was observed between both types of results during the first stages of the breaking process.