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 ($\le 20\text{/}$) 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 $4\times {10}^4\le R{e}_{\lambda }\le 3\times {10}^6\text{/}$, we find that the inertial-range exponents (${\zeta }_p\text{/}$) of the order - $p\text{/}$ structure functions do not approach their Kolmogorov value $p\mathrm{/}3\text{/}$ as $R{e}_{\lambda }\text{/}$ increases.