Geometric Depletion of Vortex Stretching in the Extreme Intermittency Tail of Isotropic Turbulence

This is Part I of the Project Omega series. This paper resolves the extreme intermittency tail of 3D Navier-Stokes turbulence to |ω| [span_0](start_span)= 533.41 s⁻¹ using a 10^9-point DNS audit (Re_λ ≈ 433) [cite: 149-150, 163-164]. [cite_start]We document a "Geometric Depletion" mechanism where stretching efficiency R decays as |ω|-0.94. This is driven by the rotation of the vorticity vector toward the intermediate strain eigenvector e_2 [cite: 183-184, 200-201]. > [cite_start]Data Source: JHTDB isotropic1024coarse.