The interaction of turbulence in water with a deformable free surface is of interest to the studies of various environmental problems and industrial applications. A free surface can be excited by the turbulent motions underneath and as a result its roughness can manifest the structures of the underlying turbulence. For example, the vertical vortices connecting to the surface can cause surface dimples. A sufficiently strong turbulence can also generate surface waves and even cause surface breakups that generate droplets and bubbles. Meanwhile, the turbulence field is affected by the kinematic and dynamic constraints of the surface in a way different from the no-slip wall. As a result, the free-surface boundary layer has many unique features. In the presence of dominant progressive waves, the turbulence can be significantly modified by the wave straining.

Our research group has performed a systematic study on the fundamental dynamics of the free-surface turbulence. We first studied the interaction of a free surface with homogeneous turbulence underneath. Using a random force in the simulation to generate isotropic turbulence underneath a deformable surface, we showed in detail the statistics, structure, and dynamics of the flow in the surface boundary layer. We also quantified the partition of kinematic and potential energy associated with gravity and surface tension in this turbulence-wave system.

We then studied the effect of progressive waves on the homogeneous turbulence underneath. We found that the Eulerian orbital velocity of the wave generates a periodically-alternating straining field that distorts the turbulence. Also, the wave nonlinearity produces mass transport (i.e., Stokes drift) in the wave propagation direction, which leads to a mean shear from the viewpoint of Lagrangian average. We obtained the details of vorticity evolution, Reynolds stress, and turbulent kinetic energy budget in both the Eulerian and Lagrangian frames of the waves. We have also studied the Langmuir turbulence, which is generated when the waves interact with the surface-shear-driven turbulent flow. The wave effect on the vorticity evolution and the energy transfer from wave to turbulence is revealed and modeled.

In addition, we have also performed extensive studies on the air entrainment and bubble generation in wave breaking using the coupled level set and volume of fluid (CLSVOF) method. A robust and accurate algorithm is proposed for tracking bubbles and detecting their breakup and coalescence. The bubble production mechanism and their subsequence movement, such as the trajectory and residence time, are systematically investigated.

**Selected Publications:**

- Xuan, A., Deng, B. & Shen, L. (2020), “Numerical study of effect of wave phase on Reynolds stresses and turbulent kinetic energy in Langmuir turbulence,” Journal of Fluid Mechanics, Vol. 904, A17.
- Zi, D., Xuan, A., Wang, F. & Shen, L. (2020), “Numerical study of mechanisms of air-core vortex evolution in an intake flow,” International Journal of Heat and Fluid Flow, Vol. 81, 108517.
- Xuan, A., Deng, B. & Shen, L. (2019), “Study of wave effect on vorticity in Langmuir turbulence using wave-phase-resolved large-eddy simulation,” Journal of Fluid Mechanics, Vol. 875, pp.173-224.
- Guo, X. & Shen, L. (2014), “Numerical study of the effect of surface wave on turbulence underneath. Part 2. Eulerian and Lagrangian properties of turbulence kinetic energy,” Journal of Fluid Mechanics, 744, pp.250-272.
- Guo, X. & Shen, L. (2013), “Numerical study of the effect of surface wave on turbulence underneath. Part 1. Mean flow and turbulence vorticity,” Journal of Fluid Mechanics, 733, pp.558-587.
- Khakpour, H.R., Igusa T. & Shen, L. (2012), “Coherent vortical structures responsible for strong flux of scalar at free surface,” International Journal of Heat and Mass Transfer, Vol. 55, pp.5157-5170.
- Kermani, A., Khakpour, H.R., Shen, L. & Igusa T. (2011), “Statistics of surface renewal of passive scalars in free-surface turbulence,” Journal of Fluid Mechanics, Vol. 678, pp.379-416.
- Khakpour, H.R., Shen, L. & Yue, D.K.P. (2011), “Transport of passive scalar in turbulent shear flow under a clean or surfactant-contaminated free surface,” Journal of Fluid Mechanics, Vol. 670, pp.527-557.
- Guo, X. & Shen, L. (2010), “Interaction of a deformable free surface with statistically-steady homogeneous turbulence,” Journal of Fluid Mechanics, Vol. 658, pp.33-62.
- Shen, L. & Yue, D.K.P. (2001), “Large-eddy simulation of free-surface turbulence,” Journal of Fluid Mechanics, Vol. 440, pp.75-116.
- Shen, L., Triantafyllou, G.S. & Yue, D.K.P. (2000), “Turbulent diffusion near a free surface,” Journal of Fluid Mechanics, Vol. 407, pp.145-166.
- Shen, L., Zhang, X., Yue, D.K.P. & Triantafyllou, G.S. (1999), “The surface layer for free-surface turbulent flows,” Journal of Fluid Mechanics, Vol. 386, pp.167-212.
- Zhang, C., Shen, L. & Yue, D.K.P. (1999), “The mechanism of vortex connection at a free surface,” Journal of Fluid Mechanics, Vol. 384, pp.207-241.