What question did this study set out to answer?

The aim is to understand the intermittency behavior of 3D Navier-Stokes turbulence and its underlying mechanisms.

March 30, 2026Open Access

Project Omega

Key Points

The aim is to understand the intermittency behavior of 3D Navier-Stokes turbulence and its underlying mechanisms.
Conducted a 10^9-point direct numerical simulation (DNS) audit
Focused on the extreme intermittency tail of turbulence
Analyzed the decay of stretching efficiency related to vorticity dynamics
Resolved the intermittency tail to |c9| = 533.41 s^{-1}
Documented the 'Geometric Depletion' mechanism affecting stretching efficiency
Found stretching efficiency decays as |c9|^{-0.94} driven by the vorticity rotation

Abstract

This is Part I of the Project Omega series. This paper resolves the extreme intermittency tail of 3D Navier-Stokes turbulence to || span₀ (startₛpan) = 533. 41 s^-1 using a 10⁹-point DNS audit (Re_ 433) cite: 149-150, 163-164. citeₛtartWe document a "Geometric Depletion" mechanism where stretching efficiency R decays as ||^-0. 94. This is driven by the rotation of the vorticity vector toward the intermediate strain eigenvector e₂ cite: 183-184, 200-201. > citeₛtartData Source: JHTDB isotropic1024coarse.

Project Omega

Key Points

Abstract

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