One-dimensional phase-reduction analysis for identifying wake lock-on characteristics

Characterization of lock-on for periodic wake flows generally requires an extensive parametric study through experiments or simulations. We instead examine lock-on (phase synchronization) by reducing the high-dimensional wake dynamics into its one-dimensional phase dynamics. We define the phase through a sensor measurement and reveal the phase sensitivity against perturbations. With the phase sensitivity function characterized, we are able to take a convolution of this function with a chosen periodic external forcing to determine its effect of lock on. This approach reveals the phase synchronization properties of the flow, including the Arnold tongue over the perturbation frequency and amplitude. Here, we apply the phase-reduction analysis to determine the lock-on characteristics of bluff-body wakes for active flow control and unsteady body maneuvers. This one-dimensional analysis can be performed in experiments and simulations, offering a pathway to examine how unsteady periodic flows responds to external forcing.