{"id":4569,"date":"2026-10-30T01:22:14","date_gmt":"2026-10-30T08:22:14","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=4569"},"modified":"2026-10-30T02:07:50","modified_gmt":"2026-10-30T09:07:50","slug":"endogenous-vortex-realization-from-finite-latent-rotational-cores-a-source-level-threshold-model-with-application-to-tornado-formation","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/10\/30\/endogenous-vortex-realization-from-finite-latent-rotational-cores-a-source-level-threshold-model-with-application-to-tornado-formation\/","title":{"rendered":"Endogenous Vortex Realization from Finite Latent Rotational Cores: A Source-Level Threshold Model with Application to Tornado Formation"},"content":{"rendered":"\n

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

Abstract<\/h3>\n\n\n\n

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.<\/p>\n\n\n\n

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<\/p>\n\n\n\n

$$
v=\\alpha q
$$<\/p>\n\n\n\n

and<\/p>\n\n\n\n

$$
\\omega=\\nabla\\alpha\\times q+\\alpha\\tau.
$$<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Available Document<\/h3>\n\n\n\n

DOI:<\/strong> 10.5281\/zenodo.23037197<\/a><\/code><\/p>\n\n\n\n

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

Source Code and Supporting Materials<\/h3>\n\n\n\n

The Zenodo record includes selected computational materials used to generate, inspect, and verify the numerical results reported in the paper.<\/p>\n\n\n\n

Primary file:<\/strong>
Endogenous_Vortex_Realization_from_Finite_Latent_Rotational_Cores.pdf<\/code><\/p>\n\n\n\n

Version 1.0 archival research paper.<\/p>\n\n\n\n

Supporting computational packages:<\/strong><\/p>\n\n\n\n