Bursting vortex ring

We establish the relationship between the twisting number and the local twist rate of vortex lines on different vortex surfaces, which extends the helicity topological decomposition to closed vortex tubes with differential twist. By developing numerical construction and measurement methods for differential twist, and using the direct numerical simulation and vortex-surface field, we quantitatively study the vortex bursting caused by differential twist in vortex rings. Two twist waves with opposite helical chirality collide on the cross section of the vortex ring after moving towards each other. In the subsequent vortex bursting, local vortex surfaces are squeezed to form a disk-like structure coiled by strongly twisted vortex lines. We model the dynamics of vortex bursting using a Burgers-like equation to estimate the bursting time. At large Reynolds numbers or initial twisting, vortex reconnection occurs in the disk-like structures, generating smaller dipole vortex tubes. The reconnection significantly weakens the twisting of vortex lines near the disk to inhibit the secondary bursting.