Origin of anomalous scaling exponents in three-dimensional turbulence

System: statistically stationary, homogeneous, isotropic turbulence of the 3D incompressible Navier-Stokes equations at $\mathrm{Re}_{\lambda} \to \infty$. Quantity: inertial-range exponents $\zeta_{p}$ in S_p(r) = <|delta_r u|^p> ~ r^zeta_p, which deviate from the Kolmogorov 1941 value $p/3$ (measured $\zeta_{6} \sim 1.78$, approximately). Answer: a derivation of zeta_p from the Navier-Stokes equations, or from an approximation with controlled error, that reproduces measured values for p up to about 10 and identifies the flow structures responsible.

A first-principles calculation of $\zeta_{p}$ that matches high-resolution DNS and experiment within error bars for $p\ \text{up to}\ 10$.