Stability of co-axial vortex rings with implications for circumstellar clumping

The Crow instability stimulates the growth of perturbations along two interacting vortex cores. A symmetric perturbation of the vortex core position grows until its amplitude is on the order of the core separation distance, at which point the cores touch and trigger a complex vortex reconnection process that results in isolated secondary vortex structures. While generally considered in the context of wingtip vortices, other interacting vortex cores, such as those induced by the Kelvin-Helmholtz instability in circumstellar disks, may also be Crow unstable. The ensuing perturbation growth would stimulate the formation of clumps of circumstellar material, possibly promoting the formation of planetesimals. In this study, we analyze the stability of two co-axial vortex rings of equal strength. Our theory predicts dominant unstable wavenumbers, expected to set the number of clumps along the cores, consistent with the observed number of clumps along existing circumstellar disks.