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• FDF with various velocity oscillations for nonlinear dynamic characterization. • The effect of flame area oscillations on heat release perturbations is examined. • Acoustic amplification measured with a closed boundary and initial external forcing. • A low-order longitudinal combustion instability simulation is used. • The effect of nonlinear flame dynamics on combustion instability is investigated. This study examines the effect of nonlinear flame dynamics on combustion instabilities in coaxial jet flames. The flame describing function (FDF) was used to establish this nonlinearity experimentally. The FDF gain was approximately constant despite velocity oscillation changes. However, the phase difference caused constructive interference to be converted into destructive interference as the velocity oscillations increased. With a closed boundary and external forcing, the initial velocity oscillation is damped from 200 to 240 Hz and amplified from 260 to 340 Hz. In the damping frequency range, the magnitude of the initial velocity oscillation decreases as the combustion chamber length decreases. When the velocity oscillates between 260 and 340 Hz, the combustion length that shows the maximum velocity oscillation varies from 200 to 500 mm and also decreases as the forcing frequency increases. This can be related to the resonant frequency that increases as the combustion chamber length decreases. There is no damping or amplification with other excitation frequencies. The self-excited pressure oscillations also occurred at a similar frequency range, which can amplify the initial velocity oscillation, but only for a combustor length of 350 mm. The second resonant frequency calculated via low-order combustion instability simulation, OSCILOS, is within the pressure oscillation range. The growth rate computed via OSCILOS exhibited a negative value, except for a combustor length of 350 mm. The growth rate also became negative as the velocity oscillations increased from 0.15 to 0.2 m/s. This could be related to a phase difference change in the FDF. The phase difference of the FDF is varied at only 300 Hz, and changes from in-phase to out-of-phase as the velocity oscillation increases from 0.1 to 0.15 m/s. The results of this study emphasize the importance of the FDF for combustion instability analysis. [ABSTRACT FROM AUTHOR]