A fundamental limit on the balance of power in shear- and pressure-driven channel flow

When suction/blowing control is applied at a wall, it can reduce the drag to even a sub-laminar level; however, there is an energetic cost to apply such control. Is the reduction of drag worth the cost of control? This presentation extends the results of Bewley (J. Fluid Mech., vol. 632, 443-446) and Fukagata et al. (Physica D, vol. 238, 1082-1086) to show that, in pressure- and shear-driven channel flows, the power consumed by the control at the wall is always greater than the power saved due to drag reduction below the laminar level, for any control distribution. In other words, the energetically optimal control solution is to relaminarize the flow.