Machine-learned wall oscillations for drag reduction in turbulent channel flows*

Imposing stream-wise travelling waves (STW) of spanwise velocity in a channel flow is a known technique for obtaining Drag Reduction (DR). In numerical simulations, the STW is enforced by using a boundary condition on the spanwise velocity component: w=A sin(λ z – ω t). For relatively low Reynolds numbers and steady parameters (ω and λ constant), DR is obtained by generating a Stokes layer next to the wall (Quadrio M. Phil. Trans. of the Royal Soc. 369, 2011) that damps the action of the coherent structures (Jimenez J. and Pinelli A. J. Fluid Mech 389, 1999). Quadrio and co-workers (Quadrio M. et al. J. Fluid Mech 627, 2009), have compiled a drag reduction/increase map for various combinations of λ and ω. Here, we explore a different route towards DR based on the conceptual idea that time variations of λ and ω can lead to local and instantaneous manipulation of the wall regeneration cycle. To "discover" λ(t) and ω (t) (typical time-scales expected to be within the typical burst period) that lead to DR and to an effective manipulation of the wall cycle, we have used a Deep Reinforcement Learning methodology, that uses the skin friction reduction as a reward and (λ, ω) as actions. We will give further details and physical interpretations of the results during the presentation.