Turbulence as a Developmental Geometry: A Structural Reformulation of the Vorticity–Stretching Mechanism

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Autor principal: Moser, Robert A.
Formato: Recurso digital
Lenguaje:inglés
Publicado: Zenodo 2026
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author Moser, Robert A.
author_facet Moser, Robert A.
contents <p>This work establishes a structural correspondence between turbulence and Developmental Geometry (DG). The vorticity–stretching mechanism of the Navier–Stokes equations is shown to be the unique local, degree‑1 homogeneous, sign‑preserving curvature–scale coupling required by the DG balance law. The finite cascade flux induces a quadratic propagation cone in log‑scale space, and the dissipation anomaly is conjecturally identified with the DG δ−1/2 divergence. The unattainability of infinite cascade is formulated as a DG structural censorship conjecture. These correspondences arise from shared geometric invariants rather than physical assumptions, suggesting that turbulence is a natural realization of DG and that its qualitative features follow from the underlying developmental geometry.</p> <div> </div>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_19242944
institution Zenodo
language eng
publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Turbulence as a Developmental Geometry: A Structural Reformulation of the Vorticity–Stretching Mechanism
Moser, Robert A.
Dynamical Systems
Differential Geometry
Fluid Dynamics
Nonlinear Dynamics
Mathematical Physics
<p>This work establishes a structural correspondence between turbulence and Developmental Geometry (DG). The vorticity–stretching mechanism of the Navier–Stokes equations is shown to be the unique local, degree‑1 homogeneous, sign‑preserving curvature–scale coupling required by the DG balance law. The finite cascade flux induces a quadratic propagation cone in log‑scale space, and the dissipation anomaly is conjecturally identified with the DG δ−1/2 divergence. The unattainability of infinite cascade is formulated as a DG structural censorship conjecture. These correspondences arise from shared geometric invariants rather than physical assumptions, suggesting that turbulence is a natural realization of DG and that its qualitative features follow from the underlying developmental geometry.</p> <div> </div>
title Turbulence as a Developmental Geometry: A Structural Reformulation of the Vorticity–Stretching Mechanism
topic Dynamical Systems
Differential Geometry
Fluid Dynamics
Nonlinear Dynamics
Mathematical Physics
url https://doi.org/10.5281/zenodo.19242944