Annular combustors may give rise to various types of thermoacoustic/combustion
instabilities. Some of the resulting oscillations coupled by transverse and longitudinal
acoustic modes are commonly observed in practice and their suppression or reduction
is an important issue that needs to be considered. The present study is performed

on a laboratory-scale turbulent annular combustor which consists of sixteen swirl-
stabilized burners, we investigate the existence of the phenomenon of change in

criticality leading to the state of longitudinal thermoacoustic instability (TAI) when

equivalence ratio and bulk velocity are systematically varied. We also show the flame-
flame interactions and the resulting flame synchronization during different dynamical

states of combustor operation. We simultaneously measure the acoustic pressure and

CH* chemiluminescence emission of the flame using a pressure transducer and high-
speed camera, respectively. We demonstrate the criticality of Hopf bifurcations is

decided by the stabilizing or destabilizing nature of the dominant nonlinearities in
the system when the control parameters are varied. The occurrence of ruinously
large-amplitude self-sustained oscillations resulting from positive feedback between
the acoustic pressure oscillations and the heat release rate fluctuations of the flames
is known as thermoacoustic instability (TAI). Depending upon the bulk velocity, we

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observe different states with distinct dynamics when the equivalence ratio is varied
alone. These dynamical states incorporate combustion noise (CN), intermittency
(INT), low-amplitude TAI (LA-TAI), high-amplitude TAI (HA-TAI), and mixed-mode
oscillations (MMO). For low bulk flow velocities, the transition from CN to LA-TAI

through INT. For intermediate flow rates, we report that the transition from CN to HA-
TAI via INT and MMO. For high bulk flow velocities, the transition from CN to LA-TAI

via INT is followed by a secondary bifurcation from the state of LA-TAI to HA-TAI.
Secondary bifurcation has been predicted in a numerical study and shown in a laminar
burner. We report the evidence of secondary bifurcation from low-amplitude TAI to
high-amplitude TAI for a turbulent thermoacoustic system.