  Self-sustained order can emerge in complex systems due to internal feedback
between coupled subsystems. Although the general mechanisms are known, the
specific paths of transition to order can be different in distinct systems.
Here, we present our discovery of a surprisingly non-monotonic emergence of
order amidst chaos in a turbulent thermo-acoustic fluid system. Fluctuations
play a vital role in determining the dynamical state and transitions in a
system, as theorized by Prigogine. In this work, we use the framework of
complex networks and encode the amplitude scales of fluctuations in the
topology of a network. Using network entropy, we identify the amount of
uncertainty in fluctuations and use it as a measure of chaotic intensity.
Further, we show that network centrality measures capture the magnitude of
jumps in amplitude scales due to fluctuations. We find that the competition
between turbulence and nonlinear interactions leads to the non-monotonic
emergence of order amidst chaos in turbulent thermo-acoustic fluid systems.

Fluid Dynamics