  A defining feature of 3D hydrodynamic turbulence is that the rate of energy
dissipation is bounded away from zero as viscosity is decreased (Reynolds
number increased). This phenomenon - anomalous dissipation - is sometimes
called the `zeroth law of turbulence' as it underpins many celebrated
theoretical predictions. Another robust feature observed in turbulence is that
velocity structure functions $S_p(\ell) :=\langle |\delta_\ell u|^p\rangle$
exhibit persistent power-law scaling in the inertial range, namely $S_p(\ell)
\sim |\ell|^{\zeta_p}$ for exponents $\zeta_p>0$ over an ever-increasing (with
Reynolds) range of scales. This behavior indicates that the velocity field
retains some fractional differentiability uniformly in the Reynolds number. The
Kolmogorov 1941 theory of turbulence predicts that $\zeta_p=p/3$ for all $p$
and Onsager's 1949 theory establishes the requirement that $\zeta_p\leq p/3$
for $p\geq 3$ for consistency with the zeroth law. Empirically, $\zeta_2
\gtrapprox 2/3$ and $\zeta_3 \lessapprox 1$, suggesting that turbulent
Navier-Stokes solutions approximate dissipative weak solutions of the Euler
equations possessing (nearly) the minimal degree of singularity required to
sustain anomalous dissipation. In this note, we adopt an experimentally
supported hypothesis on the anti-alignment of velocity increments with their
separation vectors and demonstrate that the inertial dissipation provides a
regularization mechanism via the Kolmogorov 4/5-law.
