Locations of the peak vorticity quantifying the coaxial collision of two vortex rings with unequal initial configuration

We propose an appropriate method of characterizing the motions of vortex rings with large initial circulation ratios and small radius ratios. Two flaws are found in quantifying the motions of vortex rings investigated in our study by the vorticity centroids based on the vorticity- and vorticity moment-weighted average. The two approaches tend to underestimate the radial and axial positions. The vorticity centroid based on the location of the peak vorticity inside the vortex core is found to offer a more accurate quantification of the motion of vortex rings.