Multifractality and scale-free network topology in a noise-perturbed laminar jet*

We present experimental evidence of multifractality and scale-free network topology in a noise-perturbed laminar jet operated in the unconditionally stable regime, prior to the critical point of a supercritical Hopf bifurcation and prior to the saddle-node point of a subcritical Hopf bifurcation. For both types of bifurcation, we find that (i) the degree of multifractality peaks at intermediate noise intensities, (ii) the conditions for maximal multifractality give rise to a complex network whose node degree distribution obeys a power-law scaling with an exponent of $2 < \gamma < 3$, indicating a scale-free network topology, and (iii) the Hurst exponent and the global clustering coefficient perform to different levels of effectiveness as early warning indicators of global self-excited instability. In characterizing the noise-induced dynamics of a canonical shear flow, we demonstrate that the multifractal and scale-free network dynamics often seen in turbulent flows can also be seen in a laminar flow under specific forcing conditions.