The emergence of high-amplitude periodic oscillations is observed in various complex systems in nature and engineering. Thermoacoustic oscillations in systems comprising turbulent reactive flow exemplify such complexity in the engineering context, where the emergence of oscillatory dynamics is undesirable. Turbulent reactive flow systems undergo a transition from low-amplitude aperiodic fluctuations (disorder) to high-amplitude periodic oscillations (order) of acoustic pressure, with varying fuel-to-air ratio, represented by the global equivalence ratio as a bifurcation parameter. In this study, we perform experiments to investigate how the nature of this transition from disorder to order changes under the influence of a secondary parameter in a turbulent reactive flow in a backward-facing step combustor. In our system, we vary either the thermal power input or the flame stabilizer position from the backward-facing step as a secondary parameter and obtain two different sets of transitions. Our findings reveal five qualitatively distinct types of transitions to periodic oscillations. Of these, two types of transitions exhibit a continuous nature. Two other types of transitions consist of both continuous and discontinuous bifurcations. The last type of transition is characterized by a discontinuous bifurcation to high-amplitude periodic oscillations. We show that order can emerge through a variety of routes. The change in the nature of the transition from disorder to order is intricate and undergoes a metamorphosis from continuous to discontinuous in a complex turbulent reactive flow system. We anticipate that such metamorphosis of transition is a universal phenomenon that can also occur in other complex systems involving turbulent thermo-fluid flows.

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• Bifurcations
• Chaos
• Dynamical systems
• Time series analysis