A fundamental limit on energy savings in controlled channel flow, and how to beat it

We derive a limit on energy savings in controlled channel flow. For flow driven by pressure, shear or any combination of the two, and via wall transpiration spanwise motion, uncontrolled laminar state requires least net (accounting for energetic cost control). Thus, optimal control solution is to laminarize Additionally, we raise possibility beating this limit. By simultaneously applying show that it may be possible attain sustained sub-laminar expenditure provide necessary design criterion savings.