Numerical investigation of flow structure and air entrainment of breaking bow wave generated by a rectangular plate

Breaking bow waves entrain massive gas that generate ambient noise and produce spray and bubbly wake with whitecap. This study aims to give a quantitative description of the flow structures and bubble formation during the breaking process. We consider the breaking bow waves induced by a surface-piercing flat plate and perform simulations based on an in-house code. We employ a conservative coupled level-set and volume of fluid method to capture violent variation of the liquid-gas interface. A robust immersed boundary method is adopted to model the motion of the plate. To resolve very small flow structures associated with the wave breaking process with the available computational resources, a block-structured adaptive mesh refinement strategy is used. It is found that the predicted wave characteristics, such as wave height, wave crest location, and wave profile, are consistent with the experiment. A wide range of flow phenomena, including the thin liquid sheet, jet overturning, and splash-ups are well reproduced by the present simulation. In addition, we implement a bubble-droplet detection program to track single bubbles, and the characteristics of bubble cloud (entrained air volume, spatial distribution, and penetration depth) can be analyzed quantitatively. Three typical bubble creation mechanisms for the air entrainment process of the breaking bow wave are reported, and ensemble-averaged statistics of the bubble size distribution are presented. We also quantify the evolution of the bubble distribution and discuss the power-law scaling during the bow wave breaking process.