On inertial-range scaling laws

Details On inertial-range scaling laws On inertial-range scaling laws

1995-08-03

arxiv.org/abs/chao-dyn/9507011v1

Nonlinear Sciences

Chaotic Dynamics

16 pages, postscript (uncompressed, not encoded)

Scientific paper

10.1017/S0022112096001279

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.

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