Effect of Colored Noise on Coupled Thermoacoustic Oscillators

Abstract: Stochastic fluctuations are inherent to thermoacoustic systems operating under turbulent combustion. Heat release and flow disturbances continuously perturb the acoustic field. In this study, we examine the influence of colored noise on amplitude death (AD) in coupled thermoacoustic systems. AD corresponds to the complete suppression of self-sustained thermoacoustic oscillations. The system consists of two coupled horizontal Rijke tube oscillators with time-delay and dissipative coupling. Stochastic forcing is modeled using an Ornstein-Uhlenbeck process, allowing independent control of noise intensity and correlation time. We find that increasing noise intensity gradually smooths the transition from limit cycle oscillations (LCO) to AD. It also reduces the extent of the AD regions. In contrast, the qualitative bifurcation structure remains largely unaffected by the correlation time of the colored noise. From coherence factor analysis, we find both white and colored noise induced coherence near bifurcation thresholds. The maximum coherence occurs when the correlation time is comparable to the acoustic time scale. For both shorter and longer correlation times, the coherence is reduced. These results highlights the robustness of coupling induced AD under realistic noisy conditions for effective control of thermoacoustic instabilities. Further, the coherence factor can serve as a potential early warning indicator of thermoacoustic instability in coupled thermoacoustic systems.