Inertial- and dissipation-range asymptotics in fluid turbulence

Abstract

We propose and verify a wave-vector-space version of generalized extended self-similarity [R. Benzi et al., Europhys. Lett. 32, 709 (1995)] and broaden its applicability to uncover intriguing, universal scaling in the far dissipation range by computing high-order ( ≤20) structure functions numerically for (1) the three-dimensional, incompressible Navier-Stokes equation (with and without hyperviscosity) and (2) the Gledzer-Ohkitani-Yamada shell model for turbulence. Also, in case (2), with Taylor-microscale Reynolds numbers 4× 10⁴≤Re_λ≤3× 10⁶, we find that the inertial-range exponents ( ζ_p) of the order- p structure functions do not approach their Kolmogorov value p/3 as Re_λ increases.