Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence

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 \(4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/\), we find that the inertial-range exponents (\(\zeta_{p}\/\)) of the order - \(p\/\) structure functions do not approach their Kolmogorov value \(p/3\/\) as \(Re_{\lambda}\/\) increases.