看下图，一些实验研究已经证明，这种海浪拍打过程卷吸进的气泡具有尺寸分布。见过很多文献，都是用的DNS直接模拟研究的，结果也都能证实。

但目前我想的是，能否用PBE模型，或者其他类似模型做相关的研究。

气泡直径和分布的关系

一些参考文献

Deike, L., Melville, W. K. & Popinet, S. 2016. Air entrainment and bubble statistics in breaking waves. J. Fluid Mech. 801, 91–129.
Wang, Z., Yang, J., Stern, F., 2016. High-fidelity simulations of bubble, droplet and spray formation in breaking waves. J. Fluid Mech. 792, 307–327.
G. Soligo, A. Roccon, and A. Soldati, Breakage, coalescence and size distribution of surfactant-laden droplets in turbulent flow, J. Fluid Mech. 881, 244 (2019).
Ahmed, Z., Izbassarov, D., Costa, P., Muradoglu, M., Tammisola, O. 2020. Turbulent bubbly channel flows: Effects of soluble surfactant and viscoelasticity, Computers & Fluids 212, 104717.