Non-modal analysis of coaxial jets

In this work, we investigate the subcritical behaviour of a coaxial jet subject to small-amplitude perturbations at the inflow. We use the results of optimal harmonic analysis and dynamic-mode decomposition (DMD) of the flow fields at a Reynolds number, based on the diameter and maximum velocity of the inner inlet pipe, of $Re=200$ , to show that, for a sufficiently low value of the Reynolds number, the coherent structures appearing in the perturbed dynamics of the nonlinear system can be effectively described in terms of the harmonic response of the flow. We also show that, for larger subcritical values of the Reynolds number, $Re=400$ , a huge amplification of disturbances quickly makes nonlinear effects relevant. Large-scale, near-field coherent dynamics can be still interpreted as an evidence of the preferred response of the system, using DMD of the flow to describe the noise-driven transition to turbulence downstream. The influence of the axial velocity ratio and the rotational motion of the outer stream are assessed as well. Harmonic analysis successfully predicts the prevalence of rotating helical structures observed in the columnar flow for moderate swirl of the outer jet. Finally, we compare the receptivity of the nonlinear system to the optimal linear perturbations with its response to stochastic forcing. Optimal forcing is still more effective than white noise in driving the system to a turbulent state, where nonlinear dynamics prevails. We still conclude that linear optimal forcing may be relevant in investigating the transition to turbulence in coaxial jets, even if more about the transition process could be learnt from a more expensive nonlinear analysis.