Three-Dimensional Navier–Stokes Turbulence: Deconstruction of Classical Empirical Closures and Deterministic Solenoidal Vorton Dynamics on an Attractor of Dimension Re3/4

Classical turbulence models rely on empirical statistical closures—such as eddy viscosity, Reynolds stress truncations, and subgrid parameterizations—that lack first-principles derivations, require empirical calibration, and fail to preserve exact vorticity structure. Discretizing the three-dimensional Navier-Stokes vorticity field into solenoidal vorton dipoles resolves this indeterminacy by enforcing velocity incompressibility and vorticity solenoidality simultaneously. Lagrangian vorton chains achieve natural core self-regularization without artificial Eulerian smoothing kernels: on-axis singular induction vanishes through the collinear alignment of adjacent dipoles, overlapping dipole tails synthesize an effective core scale equal to the inter-node separation, and vortex stretching dynamically dilates node spacing in exact proportion to circulation amplification. Viscous reconnection operates as an intrinsic topological phase transition that redistributes enstrophy across admissible modes, ensuring strict energy passivity and recovering anomalous dissipation without empirical viscosity. Because intense vorticity concentrates along a codimension-two filament skeleton rather than filling three-dimensional space, the dynamical attractor dimension scales with the Reynolds number to the three-quarters power, terminating the infinite moment hierarchy algebraically on a finite-dimensional phase space