Under certain operating conditions, many combustion systems in aerospace propulsion and land-based power generation exhibit large-amplitude pressure oscillations coupled with unsteadiness in the combustion processes. This unsteady multi-scale phenomenon is generally referred to as thermo-acoustic instability. Recently, model-based active control approaches are being pursued to suppress the potentially destructive instability and for this purpose a fundamental understanding of the coupling mechanisms between the dynamics of the flame and acoustics is critical.