Coherence resonance in low-density jets

Abstract

Coherence resonance (CR) is a phenomenon in which the response of a stable nonlinear system to external noise exhibits a peak in coherence at an intermediate noise amplitude. We report the first experimental evidence of CR in a hydrodynamic system, a low-density jet capable of undergoing both supercritical and subcritical Hopf bifurcations. By applying noise to the jet in its unconditionally stable regime, we find that, for both types of bifurcation, the coherence factor peaks at an intermediate noise amplitude and increases as the stability boundary is approached. We also find that the autocorrelation function decays differently between the two types of bifurcation, indicating that CR can reveal information about the nonlinearity of a system even before it bifurcates to a limit cycle. We then model the CR dynamics with a stochastically forced van der Pol oscillator calibrated in two different ways: (i) via the conventional method of measuring the amplitude evolution in transient experiments and (ii) via the system-identification method of Lee et al. (J. Fluid Mech., vol. 862, 2019, pp. 200–215) based on the Fokker–Planck equation. We find better experimental agreement with the latter method, demonstrating the deficiency of the former method in identifying the correct form of system nonlinearity. The fact that CR occurs in the unconditionally stable regime, prior to both the Hopf and saddle-node points, implies that it can be used to forecast the onset of global instability. Although demonstrated here on a low-density jet, CR is expected to arise in almost all nonlinear dynamical systems near a Hopf bifurcation, opening up new possibilities for the development of global-instability precursors in a variety of hydrodynamic systems.

Stochastic modelling of a noise-driven global instability in a turbulent swirling jet

“…To the best of the authors' knowledge, there are no applications of stochastic methods to describe the characteristics of a global hydrodynamic instability besides the work of Zhu et al (2019) and Lee et al (2019). In contrast to their work, the current investigation does not rely on external forcing of the flow but utilises the background turbulence as intrinsic stochastic forcing.…”

“…2020). The investigations of Zhu, Gupta & Li (2019) and Lee et al. (2019) revealed that the bifurcation, leading to the global instability of a low-density jet, can be characterised from the evaluation of stochastic forcing in the stable regime of the flow.…”

“…To the best of the authors’ knowledge, there are no applications of stochastic methods to describe the characteristics of a global hydrodynamic instability besides the work of Zhu et al. (2019) and Lee et al. (2019).…”

Asynchronous and synchronous quenching of a globally unstable jet via axisymmetry breaking

“…Subcritical Hopf bifurcations can arise in various flow systems (e.g. plane Poiseuille flow, Taylor-Couette flow, a Rijke tube;Reynolds & Potter 1967;Marques & Lopez 2006;Rigas et al 2016), but they have only recently been discovered in low-density inertial jets(Zhu et al 2017(Zhu et al , 2019. (iii) In regime III (562 <…”

System identification near a hopf bifurcation via the noise-induced dynamics in the fixed-point regime

“…the subthreshold regime) prior to a subcritical Hopf bifurcation (see figure 1.6), and suggested that CR can be used to forecast the onset of thermoacoustic instability. Along similar lines, Zhu et al (2019) reported CR in a prototypical hydrodynamic system (an axisymmetric lowdensity jet) and used CR to forecast the onset of global instability. However, CR-based forecasting techniques share the same limitation as the other precursors discussed in §1.2:…”