System identification of a low-density jet via its noise-induced dynamics*

Low-density jets are central to many natural and engineering processes.  Under certain conditions, they can develop global oscillations at a limit cycle, behaving as a prototypical example of a self-excited hydrodynamic oscillator.  In this study, we perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points.  We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries), and (iii) the resulting limit-cycle oscillations.  The only assumption made about the system is that it obeys a Stuart-Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems.  This study constitutes the first experimental demonstration of system identification using only the noise-induced dynamics in the unconditionally stable regime, opening up new possibilities for the prediction and analysis of the stability and nonlinear behavior of hydrodynamic systems.