Direct Numerical Simulation of Shallow Water Breaking Waves Generated by Wave Plate

Abstract

We present direct numerical simulation of breaking waves in shallow water generated by the wave plate. The open-source Basilisk solver is used to solve the incompressible, variable-density, twophase Navier-Stokes equations with surface tension. The air-water interface is advected using a momentum-conservative Volume-of-Fluid (MCVOF) scheme. The surface tension is treated with the balanced-force technique. Adaptive mesh refinement (AMR) scheme is employed for computational efficiency, concentrating the computational resource on the significant solution area. By reconstructing the piston-type wave plate numerically, we realize high-fidelity simulation of experimental waves under the wide-ranging motions of the wave plate. The relationship between varying maximum wave plate speed and associated maximum wave height before breaking is investigated, the onset of wave breaking as a function of the ratio of wave height to water depth is determined to distinguish between non-breaking waves, spilling breakers, and plunging breakers. A typical plunging breaking wave with a large ratio of wave height to water depth is initialized to recognize the wave breaking and air entrainment process. We obtain good collapse of the simulated free-surface evolution and velocity fields with respect to the experiment. The shape and size of air entrapped at impact by plunging jet matches closely the experimental observation during wave breaking. The time-evolving energy budget and bubble characteristics under breaking waves are further discussed based on the numerical results.