Gaseous cellular detonation is unsteady, and its propagation dynamics in a uniform mixture have been widely studied, but there are few works on cellular detonations in continuously disturbed media. Based on two fundamental propagation modes: stable (with regular cells) or unstable (with irregular cells), this study uses the Euler equations coupled with a two-step chemical reaction model to investigate two-dimensional cellular detonations with longitudinal disturbances. Disturbed detonations are generated by introducing a longitudinal sinusoidal density disturbance whose bifurcation parameter is the disturbance wavelength λ. The detonation cell distributions and propagation features are analyzed by recording the maximum local pressure and presenting the frequency spectrum of the averaged cell pressure. It is observed that the ratio of longitudinal disturbance wavelength λ to reaction zone width $W_{\mathrm{R}}$ plays an important role in cell morphology. For regular detonations, the cell scale changes periodically with the disturbance cycle, and the fundamental frequency of the averaged pressure signals is consistent with the disturbance frequency when this ratio is much greater than 1. If the ratio has a single-digit value, the original coupling relationship of shock waves and reaction fronts is destroyed and rebuilt, leading to an intermittent and local detonation decoupling and reinitiation. The size of newly formed large cells reaches about 3–6 times the size of the undisturbed cell. However, there are different cell-size spectra for stable and unstable detonations attributed to different transverse wave regularities. By introducing acoustic impedance analyses, the interaction of the detonation wave and varying density interface is presented, and the role of a sinusoidal density disturbance in wave dynamics is discussed.

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• Combustion
• Detonation
• High-speed flow
• Shock waves