TRANSITIONS TO CHAOS IN A FORCED JET - INTERMITTENCY, TANGENT BIFURCATIONS AND HYSTERESIS

Experimental studies of a forced transitional jet at moderate Reynolds numbers reveal interesting transitions between low-dimensional states , namely tangent bifurcations, intermittency and hysteresis. The exper iments were carried out in an axisymmetric air jet with a laminar top- hat exit profile in the low-noise ambient of a large anechoic chamber, using forcing amplitude and frequency as control parameters. Tangent bifurcations are seen to occur in two different transitions from perio dicity to chaos: (i) from stable pairing to nearly periodic modulation s of pairing and (ii) from stable double pairing to a quarter-harmonic chaotic attractor. In case (i), an empirically derived mapping closel y reproduces the temporal dynamics of one chaotic attractor at a point just after the tangent bifurcation. In case (ii), the intermittency w as characterized by estimating the scaling exponent of the p.d.f, of t he periodic durations, which was found to be close to the characterist ic value for type-II intermittency. Hysteresis is seen at higher Strou hal numbers in the transitions between aperiodic modulations and the p eriodic/chaotic double pairing states. Based on simultaneous flow visu alization and velocimetry, the hysteresis appears to be associated wit h intermittent tilting of(otherwise) axisymmetric vortices. These tran sitions are explained in terms of feedback-driven dynamics from vortex roll-ups and pairings, which can be phase-locked (periodic) or unlock ed (nearly quasi-periodic and chaotic). The observed transitions conne ct large regions of deterministic behaviour in the phase diagram, conf irming the existence of a low-dimensional dynamical system in transiti onal jets an open flow of technological relevance. Two-point coherence measurements indicate that spatial coupling (and, hence, coherent mot ion from pairing dynamics) extends for five to eight diameters from th e exit, well beyond the locations of pairing and double pairing. This justifies the use of single-point measurements and confirms our hypoth esis that the dynamics in this convectively unstable flow are primaril y temporal rather than spatio-temporal.