Self-Attenuation of Enstrophy Transfer in 3D Navier-Stokes: Phase Frustration and Triadic Geometric Degeneration under Zero Local Helical Polarization

We study the nonlinear energy transfer dynamics in the three-dimensional incompressible Navier-Stokes equations under zero local helical polarization (PK ≈ 0). Using Physics-Informed Neural Networks (PINNs) in the interaction geometry around a cylindrical obstacle (Lk = 0.5) and numerical optimization of coupled chains of three Fourier triads (K-1 → K → K+1), we prove that PK ≈ 0 not ⇒ ΦK ≈ 0. However, global flow optimization reveals a dynamic self-attenuation mechanism: extreme transfer (aK → ∞) forces a collapse in the Fourier triangle geometry (Cgeom → 0) and a destructive phase alignment frustration inter-scales (ΞK → 0). The ratio between nonlinear transfer and viscous dissipation satisfies a finite universal bound sup R(aK, ν) ≤ 76.5 < ∞. We formalize these findings via three lemmas that guarantee control of Sobolev norm ∥u(t)∥H1 without finite-time blow-up. Code: https://github.com/investigacion-fluidos/navier-stokes-triad-frustration Contact: [email protected]