Direct numerical simulation of two-way coupled microbubble and flow dynamics beneath surface waves

We present a direct numerical simulation model that couples the dynamics of microbubbles with the boundary-layer turbulence beneath surface waves. This study extends the algorithm of Tsai and Hung (J. Geophys. Res., 2007), which only simulated the flow. We implement a two-way coupled Eulerian-Lagrangian approach to model microbubbles. This framework tracks microbubbles using the Lagrangian description, influenced by the flow. Concurrently, the flow is solved in the Eulerian frame, accounting for the bubbles' backaction via point-force approximation. The component modeling the motion of the microbubbles is validated by observing the terminal velocity of free-rising bubbles and the convergence of bubble trajectories as the bubbles rise in progressive waves. The impact of bubble forcing is verified through approximate solutions. With the model validated, we conduct simulations to examine the effects of microbubbles on the flow and vice versa. Microbubbles are released into waves to analyze how the waves affect the mean rising velocity of the bubbles. Additionally, simulations of microbubbles in wind-driven turbulence demonstrate the potential for studying interactions between microbubbles and turbulence beneath wind waves.