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 |\omega| [span_0](start_span)= 533.41 \text{ s}^{-1} using a 10^9-point DNS audit (Re_\lambda \approx 433) [cite: 149-150, 163-164]. [cite_start]We document a "Geometric Depletion" mechanism where stretching efficiency R decays as |\omega|^{-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.