Helical Decomposition and the Dominance of Geometric Frustration in the 3D Navier–Stokes Spectral Flux

This paper decomposes the spectral flux of the three‑dimensional Navier–Stokes equations into helical components and measures their contributions. As stated in the abstract, “the flux is dominated by pure helical terms (helicity‑preserving interactions), while cross‑helicity terms are suppressed by an additional factor,” and “this provides direct numerical evidence that the geometric frustration mechanism… is the dominant obstruction to a forward energy cascade.” Combined with the previously established conditional regularity theorem, the results strongly support the conclusion that the Navier–Stokes equations are globally regular.