  The real Schur form (RSF) of a generic velocity gradient field $\nabla
\mathbf{u}$ is exploited to expose the structures of flows, in particular our
field decomposition resulting in two vorticities with only mutual linkage as
the topological content of the global helicity (accordingly decomposed into two
equal parts). The local transformation to RSF may indicate alternative
(co)rotating frame(s) for specifying the objective argument(s) of the
constitutive equation. When $\nabla \mathbf{u}$ is uniformly of RSF in a fixed
Cartesian coordinate frame, i.e., $u_x = u_x(x,y)$ and $u_y = u_y(x,y)$, but
$u_z = u_z(x,y,z)$, the model, with the decomposed vorticities both frozen-in
to $\mathbf{u}$, is in between two-dimensional-three-component (2D3C) and 3D3C
ones and may help curing the pathology in the helical 2D3C absolute
equilibrium, making the latter effectively work in more realistic situations.
