Transitions to chaos in a forced jet: intermittency, tangent bifurcations and hysteresis

Abstract

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 experiments 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 periodicity to chaos: (i) from stable pairing to nearly periodic modulations of pairing and (ii) from stable double pairing to a quarter-harmonic chaotic attractor. In case (i), an empirically derived mapping closely reproduces the temporal dynamics of one chaotic attractor at a point just after the tangent bifurcation. In case (ii), the intermittency was characterized by estimating the scaling exponent of the p.d.f. of the periodic durations, which was found to be close to the characteristic value for type-II intermittency. Hysteresis is seen at higher Strouhal numbers in the transitions between aperiodic modulations and the periodic/chaotic double pairing states. Based on simultaneous flow visualization and velocimetry, the hysteresis appears to be associated with intermittent tilting of (otherwise) axisymmetric vortices. These transitions are explained in terms of feedback-driven dynamics from vortex roll-ups and pairings, which can be phase-locked (periodic) or unlocked (nearly quasi-periodic and chaotic). The observed transitions connect large regions of deterministic behaviour in the phase diagram, confirming the existence of a low-dimensional dynamical system in transitional jets-an open flow of technological relevance.Two-point coherence measurements indicate that spatial coupling (and, hence, coherent motion from pairing dynamics) extends for five to eight diameters from the exit, well beyond the locations of pairing and double pairing. This justifies the use of single-point measurements and confirms our hypothesis that the dynamics in this convectively unstable flow are primarily temporal rather than spatio-temporal.