  Computational simulations of turbulent flows indicate that the regions of low
dissipation/enstrophy production feature high degree of local alignment between
the velocity and the vorticty, i.e., the flow is locally near-Beltrami. Hence
one could envision a geometric scenario in which the persistence of the local
near-Beltramy property might be consistent with a (possible) finite-time
singularity formation. The goal of this note is to show that this scenario is
in fact prohibited if the sine of the angle between the velocity and the
vorticty is small enough with respect to the local enstrophy.
