Information-theoretic control of wall-bounded turbulence

Information theory is applied to devise optimal control strategies for wall-bounded turbulence. The case considered is opposition-flow control for drag reduction in a turbulent channel flow. The design parameters are the wall-normal sensor location and the actuator amplitude of the wall jet. The cost functional depends on the Kullback-Leibler (KL) divergence of the wall stress distribution and the mutual information between the actuator and the wall-shear stress. The working principle of our approach differs significantly from traditional optimization methodologies. In the latter, the cost functional is explicitly constructed from the partial differential equations governing the system, whereas the information-theoretic approach is formulated in terms of the Shannon entropy of the flow state. It is shown that maximum drag reduction is achieved for controllers with maximum mutual information and minimum KL divergence. Our results establish the capabilities of information theory as a new venue for optimal control in wall-bounded turbulence.