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The interaction of vortex rings represents one of the most fundamental flows for elucidating the generation of vortex-induced sound. Previous studies have emphasised the radial motion of vortex rings as the dominant factor contributing to sound source. However, during the ‘slip-through’ interaction of vortex rings with unequal strengths, we observe that axial motion intensity significantly surpasses that of radial motion. This suggests that the relationship between vortex ring dynamics and sound source must be re-examined across a broader parameter space. The objective of this study is to refine the mechanism of sound generation by vortex ring dynamics. Using numerical simulations, we systematically investigate the interaction process and sound source variations of viscous vortex rings under different initial circulation ratios and radius ratios. By expressing the acceleration and deceleration of vortex rings via the time derivative of the vorticity centroid, we identify the axial velocity magnitude as the key kinematic parameter governing the contribution of each ring to sound source. Furthermore, we analyse a previously reported phenomenon wherein the weaker ring dominates the overall sound output. It occurs only within a limited range of small initial radius ratios where the magnitude of the axial velocity of the weaker ring is higher than that of the stronger ring due to the intense interaction between vortex rings. When the initial radius ratio is large, the mild interaction between vortex rings does not change the relative magnitude between the axial velocity of vortex rings. The dominance of the weaker ring in generating sound source does not occur.
Zang et al. (Fri,) studied this question.