Cross-variable amplitude-frequency coupling during intermittency in a turbulent thermoacoustic system

We investigate flame–acoustic interactions in a turbulent combustor during the state of intermittency before the onset of thermoacoustic instability using complex networks. Experiments are performed in a turbulent bluff-body stabilised dump combustor where the inlet airflow rate is varied quasi-statically and continuously. We construct a natural visibility graph from the local heat release rate fluctuations ( $\dot {q}'$ ) at each location. Comparing the average degree during epochs of high- and low-amplitude acoustic pressure oscillations ( $p'$ ) during the state of intermittency, we detect frequency modulation in $\dot {q}'$ . Through this approach, we discover unique spatial patterns of cross-variable coupling between the frequency of $\dot {q}'$ and the amplitude of $p'$ . The frequency of $\dot {q}'$ increases in regions of flame anchoring owing to high-frequency excitation of the flow and flame during epochs of high-amplitude $p'$ dynamics. However, the frequency of $\dot {q}'$ decreases in regions associated with flame-front distortions by large coherent vortices. In experiments with continuously varying airflow rates, the spatial pattern of frequency modulation varies with an increase in the average amplitude of $p'$ owing to an increase in the epochs of periodic $p'$ dynamics and the size of vortices forming in the flow. Dynamic shifts in the location of flame anchoring induce low-frequency fluctuations in $\dot {q}'$ during very-high-amplitude intermittent $p'$ dynamics. Our approach using conditional natural visibility graphs thus reveals the spatial pattern of amplitude-frequency coupling between the co-evolving flame and the acoustic field dynamics in turbulent reacting flows.