Finite-Time Blow-Up in an Axisymmetric Swirling Vortex Model and the Role of Swirl in Overcoming Geometric Frustration

This paper presents numerical evidence of finite-time blow-up in an axisymmetric model consisting of two interacting vortex rings with opposite swirl. As stated in the abstract, “the maximum vorticity grows from 10 to over 200 in a finite time T0∼0.64” and “the blow-up is absent when the swirl is removed.” The model retains the vortex-stretching mechanism of the three-dimensional Navier–Stokes equations while avoiding the geometric frustration that suppresses singularities in vector shell models. Grid-refinement tests confirm that the singularity is not a numerical artefact. The results suggest that intense swirl can bypass the geometric barriers that protect regularity in simpler vector models, offering a potential pathway toward a Navier–Stokes singularity.