{
  "abstract": "Stagnation curves of arbitrary shape (zeros of $\\mathbf v(\\mathbf x,t)$) are non-generic yet common; we derive their motion. Differentiating $\\mathbf v=\\mathbf0$ gives $\\mathbf L\\mathbf U=-\\mathbf a$ ($\\mathbf U$ curve velocity, $\\mathbf a=\\mathbf v_t$, $\\mathbf L=\\nabla\\mathbf v$ kills tangent, acts on normal plane via $2\\times2$ block $\\mathbf K$); dynamics enters only via $\\mathbf a$. Normal velocity: $-\\mathbf K^{-1}$ times normal $\\mathbf a$; tangential solvability: scalar condition $Σ=0$ per point ($Σ$: part of $\\mathbf a$ outside range $\\mathbf L$). Potential flow: $\\mathbf K$ is strain rate, normal velocity pressure gradient over principal strain rate $ε$, persistence needs uniform pressure on it. Stokes flow: tangential vorticity enters $\\mathbf K$ (centre lines), $Σ$ involves normal vorticity. Navier-Stokes: $Σ$ set by instantaneous flow via nonlocal pressure, viscosity. If $Σ\\ne0$, line becomes, to first order in $t$, isolated points at zeros of $Σ$ (critical points of $φ_t$ if potential; maybe none in Stokes flow: loops vanish). Symmetry (line an orbit of rigid-motion group, no velocity along it) suffices for persistence, not necessary: flows steady in rigidly moving frame have $Σ\\equiv0$. Incompressibility enters via $\\mathrm{tr}\\mathbf K=0$; for inviscid irrotational homentropic compressible flow, line dilatation is $φ_{tt}/c^2$, so lines can be nodes, persistence needs uniform enthalpy, singular $\\mathbf K$ arises at ordinary points, acoustic standing waves give exact examples (node line breaking into alternating sinks, saddles); also degenerate $\\mathbf K$ (pairs born at distance $O(\\sqrt t)$), curvature, torsion evolution, closure for moving-singularity-driven flows, helical and elliptically conical stagnation-point flow, exact Navier-Stokes example: saddle, centre lines split into four points per period.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26164",
  "author_total": 1,
  "authors": [
    {
      "name": "Prabakaran Rajamanickam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74bahjpatbp5x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26164",
  "fulltext_url": null,
  "id": "74bahjpatbp5x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26164",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7223036529",
  "pdf_url": "https://arxiv.org/pdf/2610.26164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74bahjpatbp5x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26164"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "How stagnation lines move, persist and break up in fluid flows",
  "title_text": "How stagnation lines move, persist and break up in fluid flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/74bahjpatbp5x",
  "venue": "arXiv",
  "versions": []
}