Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations. In the present study, we aim to study the suppression mechanism of such undesired oscillations in a pair of thermoacoustic oscillators, also known as horizontal Rijke tubes. These oscillators are coupled through a connecting tube whose length and diameter are varied as coupling parameters. With the variation of these parameters, we show the first experimental evidence of rich dynamical phenomena such as synchronization, amplitude death, and phase-flip bifurcation in coupled identical thermoacoustic oscillators. We discover that when frequency and amplitude mismatch are introduced between these oscillators, quenching of oscillations in one or both the oscillators occurs with further ease, through the mechanisms of amplitude death and partial amplitude death. Finally, we show that the effectiveness of coupling is sensitive to the dimensions of the connecting tube which can be directly correlated with the time delay and coupling strength of the system.

Intermittency observed prior to thermoacoustic instability is characterized by the occurrence of bursts of high-amplitude periodic oscillations (active state) amidst epochs of low-amplitude aperiodic fluctuations (rest state). Several model-based studies conjectured that bursting arises due to the underlying turbulence in the system. However, such intermittent bursts occur even in laminar and low-turbulence combustors, which cannot be explained by models based on turbulence. We assert that bursting in such combustors may arise due to the existence of subsystems with varying timescales of oscillations, thus forming slow–fast systems. Experiments were performed on a horizontal Rijke tube and the effect of slow–fast oscillations was studied by externally introducing low-frequency sinusoidal modulations in the control parameter. The induced bursts display an abrupt transition between the rest and the active states. The growth and decay patterns of such bursts show asymmetry due to delayed bifurcation caused by slow oscillations of the control parameter about the Hopf bifurcation point. Further, we develop a phenomenological model for the interaction between different subsystems of a thermoacoustic system by either coupling the slow and fast subsystems or by introducing noise in the absence of slow oscillations of the control parameter. We show that interaction between subsystems with different timescales leads to regular amplitude modulated bursting, while the presence of noise induces irregular amplitude modulations in the bursts. Thus, we speculate that bursting in laminar and low-turbulence systems occurs predominantly due to the interdependence between slow and fast oscillations, while bursting in high-turbulence systems is predominantly influenced by the underlying turbulence.