Flow control of three-dimensional cylinders transitioning to turbulence via multi-agent reinforcement learning.

Active flow control strategies for three-dimensional bluff bodies are challenging to design, yet critical for industrial applications. Here we explore the potential of discovering novel drag-reduction strategies using deep reinforcement learning. We introduce a high-dimensional active flow control setup on a three-dimensional cylinder at Reynolds numbers (Re_D) from 100 to 400, spanning the transition to three-dimensional wake instabilities. The setup involves multiple zero-net-mass-flux jets and couples a computational fluid dynamics solver with a numerical multi-agent reinforcement learning framework based on the proximal policy optimization algorithm. Our results demonstrate up to 16% drag reduction at Re_D = 400, outperforming classical periodic control strategies. A proper orthogonal decomposition analysis reveals that the control leads to a stabilized wake structure with an elongated recirculation bubble. These findings represent the first demonstration of training on three-dimensional cylinders and pave the way toward active flow control of complex turbulent flows.