{
  "abstract": "In viscous flow, the circulation enclosed by a deterministic material loop generally changes through vorticity diffusion. It is shown that the source-bearing unsteady Kiknadze--Krasnov vortex possesses a distinguished cylindrical material surface on which this viscous circulation transfer vanishes identically. For a single distributed mode, the scaled squared radius $x=β(t)r^2$ satisfies \\[ \\frac{\\mathrm D x}{\\mathrm D t} = 4νβ(t)\\big[(s-1)-x\\big], \\] where $β(t)$ is the inverse squared radial scale, $ν$ is the kinematic viscosity, and $s$ is the incomplete-gamma shape parameter. For $s>1$, the cylinder $x=s-1$ is transported exactly by the radial flow and preserves the inside/outside ordering of fluid trajectories. The same factor $(s-1)-x$ governs the radial vorticity gradient and the material circulation-transfer rate. Consequently, the magnitude of the distributed axial vorticity $|ω_z|$ attains its annular maximum on this material cylinder, $\\partial_rω_z=0$ there, and the enclosed circulation remains exactly $ΓP(s,s-1)$ for every admissible prescribed strain history. Neighbouring material cylinders continue to exchange circulation viscously, while the distinguished moving cylinder carries a fixed fraction of the distributed circulation throughout the admissible evolution. In the steady source--strain limit, the surface reduces to the radial stagnation cylinder. The complete velocity and pressure fields, exact radial-scale evolution, admissible parameter ranges, and qualifications for multiple radial scales are also derived. The resulting solution-specific material-circulation invariant provides an exact benchmark for numerical material-surface tracking, vortex-core evolution, and viscous circulation transport, with the principal analytical results additionally supported by machine-checked formal verification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00082",
  "author_total": 1,
  "authors": [
    {
      "name": "Khalid M. Saqr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxwfte8t4vhkh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00082",
  "fulltext_url": null,
  "id": "cxwfte8t4vhkh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00082",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7216573443",
  "pdf_url": "https://arxiv.org/pdf/2610.00082",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxwfte8t4vhkh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.00082",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00082"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A Zero-Flux Material Cylinder in the Unsteady Kiknadze--Krasnov Vortex",
  "title_text": "A Zero-Flux Material Cylinder in the Unsteady Kiknadze--Krasnov Vortex",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/cxwfte8t4vhkh",
  "venue": "arXiv",
  "versions": []
}