Bursting during intermittency route to thermoacoustic instability: Effects ofslow–fast dynamics

Intermittency observed prior to thermoacoustic instability is characterized by theoccurrence of bursts of high-amplitude periodic oscillations (active state) amidst epochsof low-amplitude aperiodic fluctuations (rest state). Several model-based studiesconjectured that bursting arises due to the underlying turbulence in the system. However,such intermittent bursts occur even in laminar and low-turbulence combustors, which cannotbe explained by models based on turbulence. We assert that bursting in such combustors mayarise due to the existence of subsystems with varying timescales of oscillations, thusforming slow–fast systems. Experiments were performed on a horizontal Rijke tube and theeffect of slow–fast oscillations was studied by externally introducing low-frequencysinusoidal modulations in the control parameter. The induced bursts display an abrupttransition between the rest and the active states. The growth and decay patterns of suchbursts show asymmetry due to delayed bifurcation caused by slow oscillations of thecontrol parameter about the Hopf bifurcation point. Further, we develop a phenomenologicalmodel for the interaction between different subsystems of a thermoacoustic system byeither coupling the slow and fast subsystems or by introducing noise in the absence ofslow oscillations of the control parameter. We show that interaction between subsystemswith different timescales leads to regular amplitude modulated bursting, while thepresence of noise induces irregular amplitude modulations in the bursts. Thus, wespeculate that bursting in laminar and low-turbulence systems occurs predominantly due tothe interdependence between slow and fast oscillations, while bursting in high-turbulencesystems is predominantly influenced by the underlying turbulence.