Turbulent wind-wave interactions have significant impacts on many applications, such as weather models in the marine environment, navigation safety of ocean vehicles, offshore energy harvesting, and forecasting of extreme wind waves, but their underlying physical mechanisms are still poorly understood. With our in-house CFD tools for turbulent flow over undulatory boundaries, we perform numerical simulations of wind-wave systems corresponding to different stages of wave evolution, namely coupled air-water DNS for early wind-wave generation, LES of wind over monochromatic waves, LES of wind over broadband waves for long-time evolution of wave field, and DNS of wind over breaking waves for the final stage of wave evolution.

In the problem of early wind-wave generation, we aim to investigate the dynamic evolutions of water waves when they are initially generated by the wind. Direct numerical simulations of a coupled air-water system are conducted to reveal the role of air turbulence on the initial water wave growth. The following figures show the wave field at three time instances. In the simulation setup, the air-water interface is flat at the beginning. As time increases, the air-water interface is distorted by the growth of wave fluctuations generated by the wind. Our study shows multiple stages of the wind-wave generation process. The surface patterns see a drastic change from the initial streak-like pattern to the eventual wave-dominant pattern.

As the wave field develops, the wave amplitude gradually becomes comparable to the length scale in the air turbulence. In this stage, the waves can cause a strong airflow perturbation in the wind, or the wave-induced airflow, which can further result in a wind-wave momentum exchange. To reveal the fundamental dynamics for the wave-induced airflow, we perform LES of turbulent wind over monochromatic waves. Based on the simulation results, the wave effects on the air are modeled analytically. The figure below shows our recent study of wind opposing waves. In the LES, we can observe the strong perturbations to the vertical air velocity by the opposingly propagating water waves. To explain the wave effects, we derived a viscous curvilinear model for a general wave boundary, which agrees well with the simulation results.

After the fundamental studies on the wind-wave interaction in the above-mentioned research, we have further investigated the behavior for the long-time development of wind-wave field. Previous studies have shown that the long-time evolution of the wave field is affected by the wind-wave momentum exchange and the nonlinear interaction between the wave components, but which mechanism plays a dominant role? To further elucidate the underlying dynamics, we perform LES of turbulent wind blowing over an irregular wave field. The simulation setup features a dynamically coupling between wind and waves, as well as a simulation duration of up to 3, 000 peak wave periods. Our study indicates that the nonlinear wave interactions dominate the wave evolution.

At the late stage of wave field evolution, the wave amplitude can grow very steep and break. Wave breaking generates ocean currents, vorticity, and turbulence and enhances the transport of mass, momentum, and energy between the atmosphere and oceans. Although the numerical method for the two-fluid simulation is relatively mature, it is challenging to conduct fine-resolution simulations of breaking waves due to the high computational cost. Previously, two-dimensional simulations were performed to study the wave breaking without using turbulence models. We perform three-dimensional direct numerical simulations of turbulent wind over breaking waves. The interface is captured using the coupled level-set and volume-of-fluid method. Our study reveals the effects of wave breaking on the momentum and energy transfer in the airflow for different wave ages and wave steepness.

**Selected Publications:**

- Cao, T. & Shen, L. (2021), “A numerical and theoretical study of wind over fast-propagating water waves,” Journal of Fluid Mechanics, Vol. 919, A38.
- Hao, X., Cao, T. & Shen, L. (2021), “Mechanistic study of shoaling effect on momentum transfer between turbulent flow and traveling wave using large-eddy simulation,” Physical Review Fluids, Vol. 6, 054608.
- Cao, T., Deng, B. & Shen, L. (2020), “A simulation-based mechanistic study of turbulent wind blowing over opposing water waves,” Journal of Fluid Mechanics, Vol. 901, A27.
- Wang, L. et al. (2020), “Surface wave effects on energy transfer in overlying turbulent flow,” Journal of Fluid Mechanics, Vol. 893, A21.
- Hao, X. & Shen, L. (2019), “Wind-wave coupling study using LES of wind and phased-resolved simulation of nonlinear waves,” Journal of Fluid Mechanics, Vol. 874, pp.391-425.
- Yang, Z., Deng, B. & Shen L. (2018), “Direct numerical simulation of wind turbulence over breaking waves,” Journal of Fluid Mechanics, Vol. 850, pp.120-155.
- Hao, X., Cao, T., Yang, Z., Li, T. & Shen, L. (2018), “Simulation-based study of wind-wave interaction,” Procedia IUTAM, Vol. 26, pp.162-173.
- Yang, D. & Shen, L. (2017), “Numerical simulation of scalar transport in turbulent flows over progressive surface waves,” Journal of Fluid Mechanics, Vol. 819, pp.58-103.
- 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.
- Yang, D., Meneveau, C. & Shen, L. (2013), “Dynamic modeling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield,” Journal of Fluid Mechanics, 726, pp.62-99.
- Yang, D. & Shen, L. (2011), “Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for multi-fluids computation,” Journal of Computational Physics, Vol. 230, pp.5510-5531.
- Yang, D. & Shen, L. (2011), “Simulation of viscous flows with undulatory boundaries: Part I. Basic solver,” Journal of Computational Physics, Vol. 230, pp.5488-5509.
- Yang, D. & Shen, L. (2010), “Direct-simulation-based study of turbulent flow over various waving boundaries,” Journal of Fluid Mechanics, Vol. 650, pp.131-180.
- Yang, D. & Shen, L. (2009), “Characteristics of coherent vortical structures in turbulence over water waves,” Physics of Fluids, Vol. 21, 125106.