Wave Dynamics

Waves are ubiquitous in various fluid mechanics systems. They play a vital role in the energy transfer in fluids. Our group actively explores the wave dynamics in oceans, lakes, and atmosphere, such as surface gravity wave evolution, wave breaking, sound wave propagation, atmospheric turbulence impact on electromagnetic wave propagation, etc. Below are two examples of our recent work on the surface wave-internal wave interaction and wave-current interaction.

When internal waves pass by, a distinct feature appears on the ocean surface with an apparent change in the roughness of the waves, which can be observed by naked eyes and marine radars on satellites images, appearing as zebra-like stripes. For over half a century, physics-based explanation of this phenomenon has been impeded by the challenge of capturing a wide range of wave motions. We recently solved this problem by simultaneously resolving the surface wave and internal wave dynamics using a two-layer ocean model on supercomputers. Besides providing the direct numerical evidence for the zebra pattern formation, our findings also show that this is an energy conservative process. The video below shows the evolution of the surface wave in the presence of an internal wave beneath the ocean surface.  

Surface roughness variations induced by internal wave
Surface roughness variations induced by internal wave

Modeling ocean surface waves under complex ocean current conditions is of crucial importance to many environmental and naval applications. For example, traveling ships and underwater vehicles generate spatially heterogeneous currents behind them through their drag and propeller motions. The strong currents can influence the surface wave pattern in the ship wake. We have developed an in-house code for high-fidelity simulations of a nonlinear phase-resolved ocean wavefield interacting with subsurface currents. The figure below shows an instantaneous wave field interacting with a ship wake. Wave-current interaction results in a reduction in the wave steepness and a smooth wake region.

Top views of the ocean wave fields in the ship wake
Top views of the ocean wave fields in the ship wake

Selected Publications:

  • Hao, X. & Shen, L. (2020), “Direct simulation of surface roughness signature of internal wave with deterministic energy-conservative model,” Journal of Fluid Mechanics, Vol. 891, R3.
  • Li, T. & Shen, L. (2020), “Safe zone for phase-resolved simulation of interactions between waves and vertically sheared currents,” Applied Mathematics Letters, Vol. 104, 106272. 
  • Li, T., Xuan, A. & Shen, L. (2020), “Study of nonlinear interaction between waves and ocean currents using high-fidelity simulation and machine learning,” Proceedings of the 33rd Symposium on Naval Hydrodynamics.