  Inertial range scaling exponents for both Lagrangian and Eulerian structure
functions are obtained from direct numerical simulations of isotropic
turbulence in triply periodic domains at Taylor-scale Reynolds number up to
1300. We reaffirm that transverse Eulerian scaling exponents saturate at
$\approx 2.1$ for moment orders $p \ge 10$, significantly differing from the
longitudinal exponents (which are predicted to saturate at $\approx 7.3$ for $p
\ge 30$ from a recent theory). The Lagrangian scaling exponents likewise
saturate at $\approx 2$ for $p \ge 8$. The saturation of Lagrangian exponents
and transverse Eulerian exponents is related by the same multifractal spectrum
by utilizing the well known frozen hypothesis to relate spatial and temporal
scales. Furthermore, this spectrum is different from the known spectra for
Eulerian longitudinal exponents, suggesting that that Lagrangian intermittency
is characterized solely by transverse Eulerian intermittency. We discuss
possible implication of this outlook when extending multifractal predictions to
the dissipation range, especially for Lagrangian acceleration.
