Thermo-acoustic instability refers to an instabiltiy arising due to acoustics field and unsteady heat release process.
[1][2][3] A very simple mechanism of acoustic amplification was first identified by Lord Rayleigh in 1878.
[4][5] In simple terms, Rayleigh criterion states that amplification results if, on the average, heat addition occurs in phase with the pressure increases during the oscillation.[1].
is the rate of heat release per unit volume (with respect to its mean value
In complex systems, Rayleigh criterion, may not ne strictly valid, as there exists many damping factors such as viscous/wall/nozzle/relaxation/homogeneous/particle damping, mean-flow effects, et, that are not accounted in Rayleigh's analysis.