  Inertial-range scaling laws for two- and three-dimensional turbulence are
re-examined within a unified framework. A new correction to Kolmogorov's
$k^{-5/3}$ scaling is derived for the energy inertial range. A related
modification is found to Kraichnan's logarithmically corrected two-dimensional
enstrophy-range law that removes its unexpected divergence at the injection
wavenumber. The significance of these corrections is illustrated with
steady-state energy spectra from recent high-resolution closure computations.
Implications for conventional numerical simulations are discussed. These
results underscore the asymptotic nature of inertial-range scaling laws.

Chaotic Dynamics;Chaotic Dynamics