Directional Depletion of Vortex Stretching: A Coherence-Modulated Dini–Morrey Profile and the Escape from the Absolute Volterra Window

Absolute vorticity profiles discard direction information that can deplete vortex stretching. This preprint studies a coherence-modulated Dini–Morrey profile for three-dimensional Navier–Stokes vorticity, with the scale weight chosen to match the stretching rate. For continuously differentiable, integrable and bounded divergence-free vorticity, the Constantin–Fefferman kernel gives an explicit stretching bound with coefficient 9/(8 pi), using the sharp geometric factor 1/2. At a fixed nonzero-vorticity center, finiteness is equivalent to a local Dini condition on the direction. Assuming a time-uniform Hölder coherence budget, a two-scale split combines the direction modulus with kinetic-energy dissipation to give a strictly subquadratic Riccati inequality and an explicit conditional persistence window. Concentrating packets retain the geometric obstruction, while oscillatory and spread families separate directional coherence from signed heat–curl cancellation under the specified companion-data bounds. Straight anti-parallel columns have zero stretching. For bent fields, a cross-product direction defect bounds the stretching rate up to an explicit logarithm, and a separate support-path hypothesis yields a lower bound for directional enstrophy dissipation. A comparison with Crow's filament-model rate is illustrative rather than a stability theorem. The depletion principle and Hölder-direction criteria are classical. The contribution is their explicit profile, constant and obstruction calibration in the series normalization. Coherence budgets and the support-path hypothesis are assumed rather than propagated from initial data; no unconditional regularity or blow-up conclusion is drawn. Version 1.0.0. The record contains the manuscript PDF, manuscript LaTeX source and a one-page visual abstract PDF. Part of the FP Science independent research program. https://fpscience.ai