Recurrence analysis of a globally unstable jet subjected to transverse acoustic forcing

In this experimental study, we take a dynamical systems approach to investigating the synchronization dynamics of a globally unstable low-density jet subjected to longitudinal and transverse acoustic forcing. On increasing the forcing amplitude, we find evidence of two classical routes to lock-in -- the saddle-node route and the torus-death route -- depending on the frequency detuning and the longitudinal/transverse nature of the forcing. Using cross-recurrence plots (CRPs) and cross-recurrence quantification analysis (CRQA), we show that the degree of complexity in the purely transversely forced jet is higher than that in the purely longitudinally forced jet. We quantify these differences in complexity using CRQA of the geometrical structures in the CRPs. We find that, compared with longitudinal forcing, transverse forcing produces lower values of the recurrence rate and determinism in the lead up to lock-in. This information could be useful for the design of open-loop control strategies for globally unstable jets.