We perform turbulence study on a number of subjects, including turbulent boundary layers, turbulent multiphase flows, turbulent atmospheric flows, upper-ocean turbulence, turbulence-particle interactions, etc. Details of these research topics can be found by following the links provided above. Below are some examples of our previous studies.

The first example of our turbulence study is the mechanism of turbulent boundary layers over wavy surfaces. This problem is of interest to many applications. Examples include atmospheric flows over hills and dunes, oceanic and estuary flows over bottom sandbars and sand ripples, locomotion biomimetics using waving plates, and wind over ocean waves.

We have studied the locomotion of a flexible wall undergoing a streamwise traveling wave motion. The objective of this study was to obtain physical insights into the swimming mechanism of certain fish for biomimetics. Using DNS, we investigated turbulence suppression, flow separation mitigation, drag reduction, and propulsion efficiency optimization.

Our research group uses DNS and LES to tackle the problem of turbulent wind over waves with a systematic approach. We first performed a mechanistic study on turbulent flows over a variety of monochromatic waves with different propagation speeds and steepness. From the simulations, we documented in detail the flow statistics to elucidate the effects of wave age and wave nonlinearity on the boundary layer. We also identified the unique vortical structures in this flow, namely reversed horseshoe and quasi-streamwise vortices if the wave propagates slowly relative to the wind or bent streamwise vortices if the wave is fast. We then studied the dynamic evolution of nonlinear waves under wind action. Our simulation captured the growth dynamics of the waves, which is essential to the understanding of wind forcing for ocean wave prediction.

The second example of our turbulence study is the interaction of turbulence in water with a deformable free surface and surface waves. This is a profound problem. The turbulence excites the free surface to produce surface wave motion and surface roughness, which can be regarded as a signature of the turbulent flow below. At the same time, the turbulence field is affected by the kinematic and dynamic constraints of the free surface. In some sense, the boundary layer at a shear-free surface can be regarded as the opposite of the boundary layer at a no-slip wall. In the presence of progressive wave, the orbital velocity of the wave generates a periodically-alternating strain rate 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.

Our research group has performed a systematic study on the fundamental dynamics of this problem. We first studied the effect of a free surface on 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 turbulence underneath. We obtained the details of vorticity evolution, Reynolds stress, and turbulent kinetic energy budget in both the Eulerian and Lagrangian frames of the waves.

**Selected Publications:**

- Deng, B., Yang, Z., Xuan, A. & Shen, L. (2020), “Localizing effect of Langmuir circulations on small-scale turbulence in shallow water,” Journal of Fluid Mechanics, Vol. 893, A6.
- Liu, Y., Shen, L., Zamansky, R. & Coletti, F. (2020), “Life and death of inertial particle clusters in turbulence,” Journal of Fluid Mechanics, Vol. 902, R1.
- Wang, L. et al. (2020), “Surface wave effects on energy transfer in overlying turbulent flow,” Journal of Fluid Mechanics, Vol. 893, A21.
- 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.
- Yang, D., He, S., Shen, L. & Luo, X. (2020), “Large eddy simulation coupled with immersed boundary method for turbulent flows over a backward facing step,” Journal of Mechanical Engineering Science, published online, 10.1177/0954406220954892.
- 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.
- Wang, L., Huang, W., Xu, C., Shen, L., Zhang, Z. (2019), “Relationship between wall shear stresses and streamwise vortices in turbulent flow over wavy boundary,” Applied Mathematics and Mechanics, 40(3), pp.381-396.
- Yang, Z., Deng, B., Wang, B. & Shen, L. (2018), “The effects of streamwise system rotation on pressure fluctuations in a turbulent channel flow,” Physics of Fluids, Vol. 30, 091701.
- Liu, C., Tang, S., Shen, L. & Dong, Y. (2017), “Characteristics of turbulence transport for momentum and heat in particle-laden turbulent vertical channel flows,” Acta Mechanics Sinica, 33, pp.333-845.
- Xuan, A., Deng, B., Cao, T. & Shen, L. (2016), “Numerical study on the effects of progressive gravity waves on turbulence,” Journal of Hydrodynamics, Vol. 28(6), pp.840-847.
- 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., 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.
- Yang, D. & Shen, L. (2009), “Characteristics of coherent vortical structures in turbulence over water waves,” Physics of Fluids, Vol. 21, 125106.
- Liu, S., Kermani, A., Shen, L. & Yue, D.K.P. (2009), “Investigation of coupled air-water turbulent boundary layers using direct numerical simulations,” Physics of Fluids, Vol. 21, 062108.
- Shen, L. (2007), “Physics of free-surface turbulence and challenges to LES,” in CFD of Multifluid Flows, von Karman Institute for Fluid Dynamics, ISSN0377-8312.
- Shen, L., Zhang, X., Triantafyllou, M.S. & Yue, D.K.P. (2003), “Turbulent flow over a flexible wall undergoing a streamwise traveling wave motion,” Journal of Fluid Mechanics, Vol. 484, pp.197-221.
- 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., 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.