Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence

Abstract

We propose and verify a wave-vector-space version of generalized extended self similarity and broaden its applicability to uncover intriguing, universal scaling in the far dissipation range by computing high-order ($\leq 20\/$) structure functions numerically for: (1) the three-dimensional, incompressible Navier Stokes equation (with and without hyperviscosity); and (2) the GOY shell model for turbulence. Also, in case (2), with Taylor-microscale Reynolds numbers $4 \times 10^{4} \leq Re_λ \leq 3 \times 10^{6}\/$, 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.