High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplet production

Abstract: [Abridged]We present high-resolution three-dimensional direct numerical simulations of breaking waves solving the two-phase Navier-Stokes equations. We investigate the role of the Reynolds and Bond numbers on the energy, bubble and droplet statistics of strong plunging breakers, and explore the asymptotic regimes at high Reynolds and Bond numbers to be compared with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to three-dimensional turbulent flow on a timescale that depends on the turbulent Reynolds number up to a limiting value of $Re_\lambda \sim 100$, consistent with the mixing transition observed in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process. We confirm two regimes in the bubble size distribution, separated by the Hinze scale $r_H$. We extend the buoyant-energetic scaling of Deike et al. (2016) to account for the cavity shape and its scale separation from the Hinze scale. We show resolved bubbles up to one order of magnitude below the Hinze scale and observe a good collapse of the numerical data compared to laboratory breaking waves (Deane and Stokes 2002). We resolve droplet statistics at high Bond number and our data show good agreement with recent experiments (Erinin et al., 2009) in various statistics. We discuss velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process.