  We show that the generalized Reynolds number (in fluid dynamics) introduced
by Ladyzhenskaya is closely related to the rotation of the positive spectral
subspace of the Stokes block-operator in the underlying Hilbert space. We also
explicitly evaluate the bottom of the negative spectrum of the Stokes operator
and prove a sharp inequality relating the distance from the bottom of its
spectrum to the origin and the length of the first positive gap.
