Data-driven methods, Nonlinear dynamics, and Transition

Ddata-driven methods have expanded the toolbox available to approach fluid problems. Deep reinforcement learning (DRL) has emerged as a particularly powerful approach to reveal new, more effective control strategies. We have used DRL to control turbulence in channel flow configurations, aiming to reduce physically relevant coherent structures in the flow.

We have also extensively used ideas from dynamical systems to study the transition to turbulence in Newtonian flows, in particular in boundary layers, which are greatly challenging due to the spatially-developing nature of the flow. Here, we identified a separatrix between laminar and turbulent states dubbed ’the edge of chaos’ as well as elements that exist within this co-dimension one manifold: ’the edge state’ (states with only one unstable directions pointing out of the edge manifold) and ‘minimal seeds’ (the most dangerous perturbations in terms of energy).

We use these ideas to better understand transition to turbulence, and to tame turbulent flows.