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This paper demonstrates cross-frequency coupling between pressure, heat release rate, fuel spray and velocity oscillations in a model aeronautical gas turbine combustor operating at a pressure of approximately 10 atm. Heat release rate was characterized by 10 kHz chemiluminescence (CL) imaging of several species. Stereoscopic particle image velocimetry and laser Mie scattering from the fuel droplets were used to measure the gas velocity and spray dynamics, respectively, at 5 kHz. The pressure fluctuations were dominated by oscillations at a frequency $f_0$, whereas the spray, CL and velocity oscillated at approximately $2f_0$. All of these oscillations were nonstationary, exhibiting changes in frequency and amplitude. Comparing the time evolution of the dominant frequencies and amplitudes indicates a behavior consistent with mutually coupled self-oscillators; the observed dynamics of the 1:2 super-harmonic coupling is consistent synchronization via oscillation death. Furthermore, increases in the frequency of the ca. $f_0$ velocity oscillations away from the harmonic ratio (increased frequency detuning) were correlated with decreases in the power of the $f_0$ pressure oscillations. The corresponding nonreacting flow had a natural hydrodynamic mode at a frequency slightly greater than $2f_0$. Hence, the data are consistent with the $f_0$ acoustic mode "pulling" the hydrodynamic frequency towards the super-harmonic ratio.