Numerical modeling of turbulent air-water mixture flows in spilling breaking waves

This paper presents a numerical study of turbulent air-water mixture flows under spilling breaking waves by using a mixture-flow model. The model is extended from the earlier 2D numerical framework NEWFLUME, which solves the Reynolds-averaged Navier-Stokes (RANS) equations for mean flow motions. The turbulence closure is accomplished by a modified k - epsilon two-equations model, in which the effect of entrained bubbles on turbulence production and dissipation is considered by incorporating additional buoyancy terms. A transient equation based on two-fluid formulation is solved for air bubble transport. The present model is validated by comparing the simulated free surface displacement, void fraction, mean velocity and turbulence kinetic energy against existing experimental data and the previous numerical results. The effects of the additional convective term in transient equation of void fraction and the bubble-induced turbulence term in turbulence transport equation are further explored. The results reveal that the additional convective term in the transient equation of void fraction plays an essential role of suppressing unphysical turbulence growth and bringing correct amount of air entrainment into water during wave breaking processes. The additional bubble-induced turbulence production and dissipation terms become effective after wave breaks when the void fraction has been appropriately modeled, and they can further reduce the simulated turbulence intensities in spilling breaking wave, rendering a better agreement with the experimental measurements.