  It is shown that, if the vorticity magnitude associated with a (presumed
singular) three-dimensional incompressible Navier-Stokes flow blows-up in a
manner exhibiting certain {\em time dependent local structure}, then {\em time
independent} estimates on the $L^1$ norm of $|\omega|\log\sqrt{1+ |\omega|^2}$
follow. The implication is that the volume of the region of high vorticity
decays at a rate of greater order than a rate connected to the critical scaling
of one-dimensional local sparseness and, consequently, the solution becomes
sub-critical.
