Swirl-Driven Vorticity Amplification Without Blow-Up in 3D Navier–Stokes: Geometric Frustration as a Universal Barrier

This paper presents direct numerical simulations of two interlaced vortex tubes with opposite swirl in the three-dimensional incompressible Navier–Stokes equations. As stated in the abstract, “the maximum vorticity grows by a factor of 3.7 (from 10.3 to 38.0) in the presence of swirl, then saturates into a statistically steady turbulent state without a finite-time singularity,” whereas “without swirl, the vorticity first decays and then slowly recovers, but the amplification is limited to a factor of 2.0.” The results are consistent with the geometric frustration mechanism previously identified in vector shell models: the cross-product structure of the nonlinearity prevents coherent forward energy transfer, even when swirl enhances vortex stretching. This provides strong evidence that geometric frustration acts as a universal barrier against blow-up in the Navier–Stokes equations.