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Endogenous Vortex Realization from Finite Latent Rotational Cores: A Source-Level Threshold Model with Application to Tornado Formation

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Internal ID: CGI-RSR-000039
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: September 29, 2026
Original Creation Date: September 16, 2026
Revised Document Date: September 29, 2026
Status: Public
Domains: Physics, Fluid Dynamics, Atmospheric Dynamics, General
Sub-Domain: Source-Level Vortex Realization / Tornado Formation
Research Topics: Vortex Realization, Latent Rotational Cores, Source Geometry, Torsion, Vorticity, Finite-Support Nucleation, Realization Thresholds, Tornado Formation, Coherence Geometry

Abstract

This paper develops a source-level model of vortex realization in which organized rotational structure may exist prior to its strong expression as observable physical flow.

The construction separates a latent transport field \(q\) and its torsion \(\tau = \nabla \times q\) from a realization field \(\alpha\). Physical velocity and vorticity are represented through

$$
v=\alpha q
$$

and

$$
\omega=\nabla\alpha\times q+\alpha\tau.
$$

This factorization allows rotational organization, realization threshold, post-threshold growth, and physical vortex intensity to be treated as distinct parts of the vortex-formation problem.

The paper develops controlled and endogenous realization models, identifies finite spatial support as a governing variable in vortex nucleation, resolves a critical finite-core realization boundary numerically, and examines the rapid post-threshold transition from latent rotational organization to strong physical vortex expression.

Tornado formation provides the principal motivating example because precursor rotational organization can precede the rapid appearance and intensification of strong near-surface flow. The mathematical construction itself is not restricted to atmospheric dynamics.

Available Document

DOI: 10.5281/zenodo.23037197

Citation:
Petersen, B. L. (2026). Endogenous Vortex Realization from Finite Latent Rotational Cores: A Source-Level Threshold Model with Application to Tornado Formation (Version 1.0). Coherence Geometry Institute. Zenodo. https://doi.org/10.5281/zenodo.23037197

Source Code and Supporting Materials

The Zenodo record includes selected computational materials used to generate, inspect, and verify the numerical results reported in the paper.

Primary file:
Endogenous_Vortex_Realization_from_Finite_Latent_Rotational_Cores.pdf

Version 1.0 archival research paper.

Supporting computational packages:

  • Vortex_Figure_Reproduction_Package.zip
    Figure-generation scripts and corresponding outputs used in the manuscript.
  • cg_finite_core_boundary_refine_extend_512_final.zip
    Refined 512 × 512 numerical package containing the critical finite-core realization boundary, underlying refinement runs, and associated boundary figure.
  • cg_finite_core_boundary_refine_extend_1024.zip
    Higher-resolution package used to verify selected critical-boundary values at 1024 × 1024 resolution.

The computational materials are supplied as archival research artifacts for inspection, reproduction, independent testing, and extension. They are not distributed as a maintained general-purpose software package.

A README file accompanying the Zenodo deposit records document provenance, scope, citation information, file integrity, and archival metadata.

Summary and Notes

Scope:

The paper addresses a general vortex-realization problem rather than proposing a complete model of any single physical vortex-forming system.

Its central distinction is between latent rotational organization and realized physical vortex intensity. A Source may contain organized transport and torsional structure while remaining only weakly expressed in observable flow. A realization field then controls the transition into strong physical velocity and vorticity.

The paper develops:

  • a source-level decomposition of latent transport, latent torsion, physical velocity, and physical vorticity;
  • finite-core latent vortex constructions with controlled spatial support;
  • bistable realization dynamics and finite-amplitude nucleation;
  • externally triggered realization experiments;
  • torsion-assisted and fully endogenous vortex-realization calculations;
  • numerical determination of the critical finite-core realization boundary \(H_{\tau,\mathrm{crit}}(a)\);
  • numerical resolution checks at 512 × 512 and 1024 × 1024 resolution;
  • post-nucleation traveling-front and critical-radius analysis;
  • realization free-energy and nucleation-barrier analysis; and
  • examination of the rapid transfer of pre-existing Source organization into observable velocity and vorticity.

A principal result is that realizability and realized intensity are not the same quantity. A broader coherent rotational Source may require weaker coupling to nucleate persistent realization even when its local peak rotational intensity is lower.

The tornado application is therefore framed as a Source-to-observable realization problem: organized rotational structure may exist before strong near-surface vortex flow becomes physically expressed.

The paper does not claim a complete atmospheric tornadogenesis model and does not replace conventional fluid-dynamical descriptions of an already realized vortex. Application to a specific physical system additionally requires the appropriate energetic and constitutive closure.

Within the broader Coherence Geometry program, the work provides a concrete example of how upstream Source organization and downstream physical realization can remain dynamically distinct.

Related Work

Foundational framework:

Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations(Version 0.1). Zenodo.
https://doi.org/10.5281/zenodo.20156531

Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical Projections. Zenodo.
https://doi.org/10.5281/zenodo.20156996

Related Source and fluid-dynamical work:

Petersen, B. L. (2026). Projection-Covariant Dynamics in Coherence Geometry: Presymplectic Reduction, Mapping-Space Evolution, and Observable Descent (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.23040342

Petersen, B. L. (2026). Coherence Geometry as a Structured Generalization of Fluid Dynamics (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.23043221

Petersen, B. L. (2026). Differential Global Coherence: Intrinsic Jet Persistence, Transport Covariance, and Projection Noncreation (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.23040056

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