## 3 Results and Discussions
### Transition of Thermoacoustic Instability Modes  
To analyze the migration characteristics of thermoacoustic oscillation modes under the stratified Ar/He jet-in-crossflow, the fast Fourier transform (FFT) analysis was performed on sound pressure oscillations under typical operating conditions (Figure 6). This study examined the thermoacoustic oscillation response at a jet aperture of 3.50 mm and a jet flow rate of 5 L/min. The Ar/He volume ratios were set to 0%/100%, 50%/50%, and 100%/0%. In the absence of stratified jet-in-crossflow, the oscillation amplitude is 25.18 Pa, with an oscillation frequency of 267 Hz (Figure 6). At an Ar/He volume ratio of 0%/100%, the oscillation amplitude decreases to 17.35 Pa. At an Ar/He volume ratio of 50%/50%, the oscillation amplitude further decreases to 14.38 Pa. Finally, at an Ar/He volume ratio of 100%/0%, the oscillation amplitude decreases to 13.14 Pa. To further explore the mode transfer characteristics of combustion thermoacoustic oscillations, a power spectral  
Figure 4: Sound pressure amplitude under the stratified Ar/He jet-in-crossflow: (**a**) diameter = 2.0 mm; (**b**) diameter = 2.5 mm; (**c**) diameter = 3.0 mm; (**d**) diameter = 3.5 mm. Figure 5: Flame CH\({}^{+}\) distribution under the stratified jet-in-crossflow with an Ar/He volume ratio of 0%/100%: (**a**) no jets; (**b**) jet flow rate = 1.0 L/min; (**c**) jet flow rate = 3.0 L/min; (**d**) jet flow rate = 5.0 L/min; (**e**) jet flow rate = 7.0 L/min. density (PSD) analysis of the oscillation signals was performed before and after the jet flow was introduced (Figure 7). The results were obtained through a short-time Fourier analysis (STFT). As the Ar/He volume ratio increases, the thermoacoustic oscillation mode undergoes significant changes (Figure 7). Although the oscillation amplitude is suppressed, the Ar/He jet-in-crossflow induces a shift in the oscillation mode (Figure 6). After the introduction of the Ar/He stratified jet, the main frequency of the thermoacoustic oscillation shifts from 267 to 265 Hz (Figure 7b). As the Ar/He volume ratio increases, the combustion chamber exhibits a multi-modal coexistence state, with an oscillation frequency at 105 Hz (Figure 7c). At an Ar/He volume ratio of 50%/50%, a second-order oscillation is observed at 264 Hz. As the Ar/He volume ratio increases to 100%/0%, more oscillation modes coexist. A PSD analysis reveals three simultaneous oscillation modes: 121, 238, and 291 Hz. These results indicate that the Ar/He jet-in-crossflow can effectively suppress thermoacoustic oscillations, induce the migration and transformation of the original thermoacoustic oscillation modes, and disrupt the coupling between flame and sound waves. A higher density of the jet gas enhances its penetration force, which reduces the intensity of flame heat-release pulsations. The changes in the flow field induced by the jet play a key role in mitigating thermoacoustic instabilities. To investigate the mode transfer mechanism of thermoacoustic oscillations, the phase difference and nonlinear dynamic characteristics of thermoacoustic oscillations were analyzed before and after the jet was introduced (Figure 8). A thermoacoustic oscillation signal  
Figure 6: FFT analysis of sound pressure under the stratified Ar/He jet-in-crossflow. Figure 7: STFT analysis of sound pressure under the stratified Ar/He jet-in-crossflow with the flow rate set to 5.0 L/min: (**a**) no jets; (**b**) Ar-0% + He-100%; (**c**) Ar-50% + He-50%; (**d**) Ar-100% + He-0%. with a duration of 0.55 s was selected, and this signal exhibited intermittent characteristics. Before the jet introduction, the absolute phase difference of the flame thermoacoustic oscillation exceeds 90\({}^{\circ}\). After the jet introduction under certain working conditions, the absolute phase difference decreases below 90\({}^{\circ}\). Before jet control, the thermoacoustic oscillation exhibits a complete limit cycle oscillation state, with the phase difference exceeding 90\({}^{\circ}\) (Figure 8a).