  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.
