  Universal properties of turbulence have been associated traditionally with
very high Reynolds numbers, but recent work has shown that the onset of the
power-laws in derivative statistics occurs at modest microscale Reynolds
numbers of the order of 10, with the corresponding exponents being consistent
with those for the inertial range structure functions at very high Reynolds
numbers. In this paper we use well-resolved direct numerical simulations of
homogeneous and isotropic turbulence to establish this result for a range of
initial conditions with different forcing mechanisms. We also show that the
moments of transverse velocity gradients possess larger scaling exponents than
those of the longitudinal moments, confirming past results that the former are
more intermittent than the latter.
