Nonlinear Dynamics of Forced Transitional Jets: Temporal Attractors and Transitions to Chaos

Abstract

Jets, although described as open flows in engineering terms due to their boundary conditions, can actually exhibit closed-flow dynamics (i.e., self-driven oscillations) in spite of their convective instabilities. An initially laminar, axisymmetric jet (4 cm air jet in the Reynolds number range 1.1 × 10⁴ ≤ Re_D ≤ 9.1 × 10⁴) was controlled with single-frequency, longitudinal, bulk excitation using two control parameters: forcing amplitude a_f (≡ u’_f/U_e, where u’_f is the exit centerline rms velocity fluctuation at the forcing frequency and U_e is the jet exit velocity) and frequency St_D(= f_exD/U_e, where f_ex is the excitation frequency and D is the jet diameter). Experimental evidence is presented for the existence of a low-dimensional temporal dynamical system (and, hence, dynamical closure) in this physically open flow, including: (i) a detailed phase diagram, (ii) well-characterized periodic and chaotic attractors, and (iii) identifiable transitions between low-dimensional states, namely tangent bifurcations, intermittency, hysteresis and an isolated branch in the experimentally determined bifurcation diagram.