Input-output framework for actuated boundary layers

This work extends the input-output approach to study actuated wall-bounded flows. In particular, we develop an analytical tool to investigate the flow response to specified geometric actuation patterns/intensities imparted through a range of temporal input signals. A superposition of point source inputs of varying intensity are used to represent the effect of given control devices on the flow field. We then take advantage of the linearity of the transfer function to build the actuated flow field as a weighted superposition of the point source responses. We validate the method through comparisons with numerical and experimental studies of transitional boundary layers subjected to a spanwise array of symmetric dielectric-barrier discharge (DBD) plasma actuators and a DBD plasma actuator operating in constricted discharge mode. We focus on the steady-state (time-averaged) flow response, which corresponds to a step response in our modeling framework. The method is shown to reproduce the streamwise velocity field, including the structural features obtained through the spanwise array of symmetric DBD actuation as well as the vortical structures observed downstream of the DBD actuator operated in constricted discharge mode. These results indicate the utility of this extension to the widely used input-output framework in analyzing the effects of particular actuation modalities used in flow manipulation. This analysis tool provides a cost-effective alternative to performing parametric studies to evaluate the relative promise of different actuator geometries and signal combinations using extensive experimental or high-fidelity simulation studies.