Coupling and synchronisation effects on local lock-in of two thermoacoustic oscillators in a stochastic environment

Flame–flame interactions in continuous combustion systems can induce a range of nonlinear dynamical behaviours, particularly in the thermoacoustic context. This study examines the mutual coupling and synchronisation dynamics of two thermoacoustic oscillators in a model gas-turbine combustor operating within a stochastic environment and subjected to external sinusoidal forcing. Experimental observations from two flames in an annular combustor reveal the emergence of dissimilar limit cycles, indicating localised lock-in of thermoacoustic oscillators. To interpret these dynamics, we introduce a coupled stochastic oscillator model with sinusoidal forcing terms, which highlights the critical role of individual synchronisation in enabling local lock-in. Furthermore, through stochastic system identification using this phenomenological low-order model, we mathematically demonstrate that a transition towards self-sustained oscillations can be driven solely by enhanced mutual coupling under external forcing. This combined experimental and modelling effort offers a novel framework for characterising complex coupled flame dynamics in practical combustion systems.