Effect of Colored Noise on Coupled Thermoacoustic Oscillators

Abstract

Noise can significantly influence thermoacoustic dynamics, yet the role of noise color in coupled thermoacoustic oscillators remains largely unexplored. Here, we examine the influence of colored noise on the dynamics of coupled thermoacoustic systems. The system consists of two coupled Rijke tube oscillators with time-delay and dissipative coupling. Stochastic forcing is modeled as an additive Ornstein-Uhlenbeck (OU) process, such that white and colored noise contain equal power within a band around the system's natural frequency. We find that noise influences the system most prominently near the transition between limit-cycle oscillations (LCO) and amplitude death (AD) states, where increasing noise amplitude smoothen the transition and reduces the extent of the AD regions. Our analysis reveals the emergence of coherence resonance near instability threshold under both white and colored noise. The peak coherence factor varies with the noise color, with the largest peak coherence observed for colored noise whose correlation time is much shorter than the acoustic time scale. White noise and the shortest-correlated OU noise exert the strongest influence on both the pressure amplitude response and the coherence resonance. Overall, our results show that, under both coupling mechanisms, colored noise induces qualitatively similar trends in the system response, governed by its amplitude and correlation time.