VORTON DYNAMICS FOR 3D NAVIER STOKES DNS AND THE SINGULAR ATTRACTOR

Classical Direct Numerical Simulation (DNS) of 3D Navier-Stokes turbulence is computationally paralyzed by volumetric grid constraints, forcing degrees of freedom to scale catastrophically at Re9/4. We present a fundamentally different framework which discards empty volumetric tracking in favor of an exact singular decomposition of the 3D Navier-Stokes vorticity field. By modeling 3D turbulence exclusively as 3D singular dipoles (vortons) evolving on a deterministic spectral manifold governed by a 72-fold gear-lock symmetry, the framework captures the exact physical engine of the turbulent cascade. Resolving only the 1D topological
skeleton of the flow triggers a massive dimensional collapse, reducing computational scaling strictly to Re3/4.
Crucially, the framework requires absolutely no artificial core regularization; the desingularization scale is dynamically dictated by the exact geometric distance between interacting dipoles. Furthermore, the historical inability of discrete vortex methods to satisfy exact boundary mechanics is solved via a dual-geometric projection utilizing image vortons and perpendicular core tubes, guaranteeing strict no-slip conditions (u = 0). Accelerated by Vortex-In-Cell (VIC) multipole expansions, this parameter-free approach abandons the phenomenological zoo of fluid modeling, providing a strict, economical, and physically transparent mathematical description of fully developed turbulence and the exact recovery of the Kolmogorov −5/3 spectrum.