Wall-bounded turbulence control: statistical characterisation of actions/states

The present paper reports the results of a Monte Carlo experiment using a turbulent channel flow. Different actions are proposed, varying the size, duration and sign of a localised volumetric force that acts near one wall of a turbulent channel flow, running at a small Reynolds ($Re_\tau=165$) in a small computational domain. The effect of each action is evaluated comparing the evolution of the flow with and without the action, gathering statistics over 1700 repetitions of the experiment for each action. The analysis of the results show that small/short forcings are equally likely to increase or decrease the skin friction drag, independently of the sign of the forcing (i.e., towards or away from the wall). When the size or the duration of the forcing increases, so does the probability of increasing the skin friction. Then, an "a priori" analysis is performed, evaluating the state of the flow just before the action, conditioned to actions that result in a decrease of the skin friction over a period of one eddy turn-over time. The resulting fields of velocity, wall shear stresses and wall pressure are consistent with an opposition control strategy, where the forcing is opposing the vertical motions near the wall. Finally, a preliminary analysis of the performance of actuation triggered by pressure or wall shear stresses sensors is evaluated (i.e., "a posteriori" analysis). Our results show that the actuation triggered by a wall shear sensor seems to be more effective than the actuation triggered by a wall pressure sensor, at least for the preliminary definitions of sensors and thresholds used here.