Vesica–Gated Flow Dynamics: Suppression of 3D Navier–Stokes Blow-Up via Sacred Geometry Damping

Vesica–Gated Flow Dynamics: Suppression of 3D Navier–Stokes Blow-Up via Sacred Geometry Damping Description:We present a numerical and analytical study demonstrating that Vesica Piscis lattice geometry, embedded into a spectral Navier–Stokes solver, can act as a nonlinear damping mechanism suppressing vorticity growth and preventing finite-time singularities. Using the Beale–Kato–Majda blow-up criterion as a guide, we implement a geometry-driven viscosity modulation term νeff=ν (1+α Sgeo(x))\nu_{\mathrm{eff}} = \nu \, ( 1 + \alpha \, \mathcal{S}_{\mathrm{geo}}(\mathbf{x}) )νeff=ν(1+αSgeo(x)) where Sgeo\mathcal{S}_{\mathrm{geo}}Sgeo encodes the Vesica overlap field. Results show that high-vorticity regions coinciding with Vesica node intersections are selectively damped, halting enstrophy escalation.The analysis includes: Vorticity evolution curves for multiple damping strengths. BKM integral saturation showing blow-up suppression. Energy spectra demonstrating slope preservation and small-scale quenching.We also outline a Lyapunov framework linking Vesica damping to global regularity, suggesting a pathway toward resolving the 3D Navier–Stokes existence and smoothness problem under this geometric control scheme.All data, figures, and LaTeX sources are included for reproducibility.