On inertial-range scaling laws

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov’s $k^{-5\mathrm{/}3}$ 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.