  This study examines the interplay between acoustic pressure oscillations and
interactions between regions of intense vorticity in the reactive field of a
turbulent combustor. These regions of intense vortical interactions are
identified as vortical communities in the network space of weighted directed
vortical networks constructed from two-dimensional velocity data. The vortical
interactions in the high-dimensional reactive flow are condensed into a
low-dimensional network representation by leveraging the inter-community
strengths and the weighted community centroids. Subsequently, we show that the
mean and the maximum of all inter-community interactions exhibit a strong
delayed correlation with the acoustic pressure oscillations during the state of
thermoacoustic instability. In contrast, during the state of combustion noise,
the correlation between the acoustic pressure oscillations and the
inter-community interactions is lost due to the incoherent spatiotemporal
behaviour of acoustic and hydrodynamic fields in turbulent thermoacoustic
system. Spatiotemporal evolution of pairs of vortical communities with the
maximum inter-community interactions provides insight into explaining the
critical regions detected in the reaction field during the states of
intermittency and thermoacoustic instability in previous studies. We further
demonstrate that the high correlations between network measures and acoustic
pressure oscillations during the state of thermoacoustic instability weaken
when steady air jets are introduced within the critical region to suppress the
thermoacoustic oscillations. This work sheds light on the intricate
relationship between the vortical interactions and the acoustic behaviour in a
turbulent combustor, thus offering insights for understanding thermoacoustic
instabilities in combustion systems and for unsteady flows in general fluid
dynamics literature.
