The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box [0, L]3 is addressed through four sets of numerical simulations that calculate a new set of variables defined by Dm(t) = (ω¯0-1 Ωm)αm for 1 ≤ m ≤ ∞ where αm = 2m/(4m - 3) and [Ωm(t)]2m = L-3 ∫ V{script} |ω|2m dV with ω¯0 = νL-2. All four simulations unexpectedly show that the Dm are ordered for m = 1, ⋯, 9 such that Dm+1 < Dm. Moreover, the Dm squeeze together such that Dm+1/Dm ↗ 1 as m increases. The values of D1 lie far above the values of the rest of the Dm, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier-Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of 40963. © 2013 Cambridge University Press.