A shallowly submerged hydrofoil often causes disturbances on the free water surface through the generation of numerous vortex structures, leading to phenomena such as surface breaking and splashing. These phenomena encompass various physical mechanisms. In this study, we employ the third-generation vortex identification technique Liutex, to conduct a detailed analysis of the vortex structures generated by the hydrofoil near the water surface. We observe that these coherent vortex structures have a strong tendency to entrain surrounding fluid, resulting in air entrainment and bubble sweep-down phenomena at the free surface. We analyze the bubble dynamics in terms of bubble number density, volume distribution, and number distribution. This analysis reveals the dynamical characteristics of bubbles under the influence of vortex structures. Additionally, by tracking the vortex structures identified by Liutex, we identify two distinct forms of air entrainment induced by the shallowly submerged hydrofoil. The results indicate that the third-generation vortex identification technique Liutex, effectively explains the mechanisms behind the hydrofoil-induced free surface breaking. Furthermore, the analysis of bubble motion using Liutex reflects the evolution and distribution patterns of characteristic scales within the turbulent flow field.