  Rocket engine combustors are prone to transverse instabilities that are
characterized by large amplitude high frequency oscillations in the acoustic
pressure and the heat release rate. We study the coupled interaction between
the acoustic pressure and the CH* intensity oscillations in a 2D multi-element
self-excited model rocket combustor during the transition from a stable state
to thermoacoustic instability through intermittency. We show the emergence of
synchronization between these oscillations from desynchronization through
intermittent phase synchronization during the onset of thermoacoustic
instability. We find substantial evidence that the intensities of the jet
flames close to the end wall is higher than that observed near the center of
the combustor as a result of its strong coupling to the local acoustic field.
Using concepts from recurrence theory, we distinguish the type of
synchronization between the acoustic pressure and the CH* intensity
oscillations at the end wall and the center of the combustor during
thermoacoustic instability. Analyzing the local CH* intensity oscillations, we
observe that the longitudinally propagating jet flames experience substantial
transverse displacement with flame merging effects during thermoacoustic
instability. Furthermore, we differentiate the interaction of the jet flames
with the shock wave during intermittency and thermoacoustic instability at both
the end wall and the center of the combustor. We also discerned the change from
stochastic to deterministic nature in the local CH* intensity oscillations
during the transition to thermoacoustic instability. Our results demonstrate
that only the first few transverse modes contribute to the generation of
acoustic power from the reacting flow, in spite of the pressure oscillations
featuring several harmonics.
