  Recently, strong evidence has accumulated that some solutions to the
Navier-Stokes equations in physically meaningful classes are not unique. The
primary purpose of this paper is to establish necessary properties for the
error of hypothetical non-unique Navier-Stokes flows under conditions motivated
by the scaling of the equations. Our first set of results show that some scales
are necessarily active -- comparable in norm to the full error -- as solutions
separate. `Scale' is interpreted in several ways, namely via algebraic bounds,
the Fourier transform and discrete volume elements. These results include a new
type of uniqueness criteria which is stated in terms of the error. The second
result is a conditional predictability criteria for the separation of small
perturbations. An implication is that the error necessarily activates at larger
scales as flows de-correlate. The last result says that the error of the
hypothetical non-unique Leray-Hopf solutions of Jia and Sverak locally grows in
a self-similar fashion. Consequently, within the Leray-Hopf class, energy can
de-correlate at a rate which is faster than linear. This contrasts numerical
work on predictability which identifies a linear rate. This discrepancy can
likely be explained by the fact that non-uniqueness can be viewed as a
perturbation of a singular flow.
