Thermo-acoustic instabilities are a challenging problem that a ects aircraft gas tur- bines, rockets, furnaces, and other con ned combustion systems (Lieuwen & Yang 2005). For these instabilities to occur, the uctuating heat release has to be su ciently in phase with the pressure. This leads to a thermo-acoustic oscillation, which usually displays itself as noise, vibrations, ame extinction and structural failure. It is, therefore, paramount for engineers to understand, predict and control these oscillations, and suppress them when they occur.