Symmetry breaking dynamics and Stuart-Landau modeling of triplet flame oscillators

Triple-flame systems serve as fundamental units for understanding multi-flame interactions, wherein symmetry-breaking dynamics reveal critical coupling mechanisms that scale to complex burner arrays. In this study, we experimentally and theoretically investigate the dynamical modes of triple flickering laminar buoyant diffusion flames arranged in an isosceles triangular configuration, bearing a reflection symmetry. To overcome the limitations of discrete geometric parameter sampling, we implement continuous translational motion of the vertex flame at a controlled velocity, while independently varying the base length and the fuel flow rate. This novel approach enables detailed observation of coupling behaviors, leading to the identification of both previously reported modes and two new symmetry-breaking modes: the asymmetric partially flickering death mode and the asymmetric partially in-phase mode. A comprehensive regime diagram, established for the first time, maps the emergence and transitions of these dynamical states, highlighting the prevalence of symmetry-breaking instabilities. The time-delay coupled Stuart-Landau oscillator model successfully reproduces most experimentally identified modes, corroborating the underlying coupling mechanisms; its limitations in representing certain decoupled or complex asymmetric regimes are also identified. Furthermore, the corresponding bifurcation analysis delineates the parameter regions of distinct dynamical modes and their transition boundaries, providing a theoretical framework for predicting symmetry-breaking dynamics in coupled flame systems.