  We decompose the velocity gradient tensor for turbulence into normal and
non-normal parts, and condition our analysis on the strain eigenvector
alignments between these tensors. We identify states that always enhance, and
always counteract the axisymmetric expansion state, and give a rationale for
decomposing the production balance term into its constituents: complex behavior
arises when the dominant strain alignments involve the non-normal tensor.
Finally, we develop a topological analysis framework where mathematical bounds
on two of the three variables leads to an analysis in two planes.
