Supplementary material from "Adaptive control of turbulence intensity is accelerated by frugal flow sampling"

The aerodynamic performance of vehicles and animals, as well as the productivity of turbines and energy harvesters, depends on the turbulence intensity of the incoming flow. Previous studies have pointed at the potential benefits of active turbulence control in closed-loop. However, it is unclear what the minimal sensory and algorithmic requirements are for realizing this control. Here we show that very low bandwidth anemometers record sufficient information for an adaptive control algorithm to converge quickly. Our online Newton–Raphson algorithm tunes the turbulence in a recirculating wind tunnel by taking readings from an anemometer in the test section. After starting at 9% turbulence intensity, the algorithm converges on values ranging from 10 to 45% in less than 12 iterations within 1% accuracy. By down-sampling our measurements, we show that very low bandwidth anemometers record sufficient information for convergence. Furthermore, down-sampling accelerates convergence by smoothing gradients in turbulence intensity. Our results explain why low bandwidth anemometers in engineering and mechanoreceptors in biology may be sufficient for adaptive control of turbulence intensity. Finally, our analysis suggests that if certain turbulent eddy sizes are more important to control than others, frugal adaptive control schemes can be particularly computationally effective for improving performance.