3D Pseudo-Spectral DNS of Kida-Pelz Vortex: Vorticity N-Scaling Data for Navier-Stokes Finite-Time Blow-Up Analysis (Phase 1)

Phase 1 simulation data from a 3D pseudo-spectral direct numerical simulation (DNS) study of the incompressible Navier-Stokes equations, investigating potential finite-time blow-up of the Kida-Pelz initial condition. This dataset supports research toward the Clay Millennium Prize Problem on Navier-Stokes existence and smoothness. The solver uses a dealiased (2/3-rule) Fourier pseudo-spectral method with Carpenter-Kennedy 5-stage 4th-order Runge-Kutta time integration on a triply-periodic domain. Computations were performed on an NVIDIA RTX 5060 Ti 16GB GPU using CuPy. Dataset includes 15 simulation runs across a parameter sweep: grid resolutions N = 256, 320, 384 at kinematic viscosities nu = 0.001, 0.0005, 0.0002, 0.0001, 0.00005. Each run contains full time series of energy, enstrophy, peak vorticity, BKM blow-up integrals, energy spectra E(k) at peak vorticity, Kolmogorov microscale diagnostics, and blow-up power-law fits. Key finding: The vorticity N-scaling exponent alpha (omega_peak ~ N^alpha) reaches alpha = 1.17 at nu = 0.0001, exceeding the critical threshold alpha = 1.0 required by the Beale-Kato-Majda criterion for finite-time singularity. This signal requires validation at N = 512 (Phase 2). Files: JSON simulation logs with full diagnostics, CSV scaling table, Python solver source code (ns_solver.py), SHA-256 integrity checksums.