Onset and equilibration of oscillations in general Rijke devices

Oscillations in Rijke devices of general shape are investigated with a model in which the relation between the acoustic motion and the heat transfer from the gauze is nonlinear. In addition to corroborating existing results on necessary conditions for the growth of small disturbances, the model predicts the observed finite range of blowing speeds that allow oscillation. The nonlinear theory determines the amplitude at which the oscillation saturates. Under some circumstances, the equilibrium amplitude is a multivalued function of the parameters, and hysteresis is possible.