Diffuse Cascade in 3D Navier–Stokes: Time-Resolved Evidence for Triad Equidistribution

We present time-resolved numerical evidence that triad amplitudes in the three-dimensional incompressible Navier–Stokes equations remain equidistributed across spectral shells and time. Across resolutions N=32, 64, and 128, no concentration events are observed under stringent diagnostics. The minimum amplitude equidistribution (AET) remains above 0.308, the scaling exponent remains near zero, and no helical sector exhibits persistent dominance. These results indicate a diffuse cascade in which energy transfer is continuously distributed across triads, with no transient or sustained concentration detected in the tested regimes. The findings challenge blowup mechanisms that rely on triad-level concentration or persistent alignment, and support a picture of the Navier–Stokes cascade as structurally resistant to spectral concentration. Keywords: Navier-Stokes, triad equidistribution, spectral concentration, diffuse cascade, Littlewood-Paley, fluid dynamics, blowup, helical decomposition