Spectral Flux Decay and Quasi‑Trapping in 3D Navier–Stokes: Numerical Evidence for a Universal Barrier

This paper measures the spectral flux of energy across wavenumber cutoffs in the three‑dimensional Navier–Stokes equations. As stated in the abstract, “for a turbulent initial field with a k^−5/3 spectrum, Π(K) is of order 10^−10 and decays with K,” and “the ratio Π(K)/E>K is of order 10^−14.” The extreme inefficiency of the forward cascade provides strong numerical support for the quasi‑trapping hypothesis introduced previously. Combined with the conditional regularity theorem, the results indicate that geometric frustration acts as a universal barrier against finite‑time blow‑up and offer a concrete pathway toward resolving the Clay Millennium Problem.