Emergence of order from chaos through a continuous phase transition.*

As the Reynolds number is increased, a laminar fluid flow transitions to a turbulent flow, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, indicated by the loss of multifractality of the acoustic pressure oscillations. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting in a nonlinear manner. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, which is defined as the fraction of the correlated dynamics, increases gradually from zero to one. Our study reveals that the variance of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that three of the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.