Strain–Vorticity Interaction and Rotational Coherence: From Magnitude Comparison to Enstrophy Production

This work develops a constraint-based framework for distinguishing kinematic strain–rotation balance from dynamical strain–vorticity interaction in incompressible fluid flow. Starting from the velocity-gradient decomposition into symmetric strain S and antisymmetric rotation \Omega, the paper examines the limitations of magnitude-based measures such as normalized strain–rotation imbalance for characterizing rotational coherence. The analysis instead centers on the exact vortex-stretching and enstrophy-production term \omega\cdot S\omega, which measures how the strain field acts on the vorticity vector. The framework connects this interaction to strain-eigenvector alignment, derives the corresponding normalized geometric bound, and examines its behavior in canonical flows including solid-body rotation, simple shear, Lamb–Oseen flow, and Burgers vortex. The Burgers-vortex example demonstrates why strain dominance need not imply suppression of rotational coherence: strain can actively sustain vorticity through vortex stretching. The work also relates the kinematic formulation to established Q, Okubo–Weiss, and Omega-type diagnostics, and distinguishes local vortex stretching from integrated enstrophy production–dissipation balance. No universal vortex threshold or parameter corridor is proposed. Instead, the results support an interaction–response interpretation in which rotational dynamics depend on strain–vorticity alignment, dissipation, transport, and forcing rather than on strain–rotation magnitude dominance alone. The contribution is intended as a technical synthesis and diagnostic framework, bringing established results into a unified constraint-based interpretation while clearly separating kinematic descriptors from dynamical interaction measures.