  Reinforcement learning is applied to the development of control strategies in
order to reduce skin friction drag in a fully developed turbulent channel flow
at a low Reynolds number. Motivated by the so-called opposition control (Choi
et al. 1993), in which a control input is applied so as to cancel the
wall-normal velocity fluctuation on a detection plane at a certain distance
from the wall, we consider wall blowing and suction as a control input, and its
spatial distribution is determined by the instantaneous streamwise and
wall-normal velocity fluctuations at the distance of 15 wall units above the
wall. Deep neural network is used to express the complex relationship between
the sensing information and the control input, and it is trained so as to
maximize the expected long-term reward, i.e., drag reduction. When only the
wall-normal velocity fluctuation is measured and a linear network is used, the
present framework successfully reproduces the optimal linear weight for the
opposition control reported in the previous study (Chung & Talha 2011). In
contrast, when a non-linear network is used, more complex control strategies
based on the instantaneous streamwise and wall-normal velocity fluctuations are
obtained. Specifically, the obtained control strategies abruptly switch between
strong wall blowing and suction for downwelling of a high-speed fluid toward
the wall and upwelling of a low-speed fluid away from the wall, respectively.
The obtained control policies lead to drag reduction rates as high as 37 %,
which is higher than 23 % achieved by the conventional opposition control at
the same Reynolds number. The present results indicate that reinforcement
learning can be a novel framework for the development of effective control
strategies through systematic learning based on a large number of trials.
