Two-dimensional Navier–Stokes simulation of breaking waves

Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation. The numerical modelling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account as a stress tensor computed from gradients of the volume fraction function. Preliminary results concerning the time evolution of liquid–gas interface and vorticity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Different evolutions of the wave energy are observed during the breaking stage. The energy dissipation due to viscosity becomes significantly important at each time of the impact of jet and the formation of splash-up. It is found that nearly 70% of the wave energy is lost after about three periods.