{
  "abstract": "Streaming from a deforming cavity wall serves micromixing, pumping and particle handling. We solve it in closed form in a two-dimensional circular cavity, for any azimuthal wall mode $m$, as $\\mathrm{Wo}^2 \\to 0$. A biharmonic inversion against the Reynolds stress, corrected by the second-order slip a moving wall imposes, gives the Lagrangian mean a tracer follows for a deforming no-slip wall, $ψ_L = -[m(5m+4)a_m^2/(128(m+2)(2m+1))]\\,r^{2m}(r^2-1)^2\\sin 2mθ$, with a companion form for a shear-free interface. For a single mode the factor $(5m+4)/(m+2)$ relating it to the auxiliary solution $ψ_2$ is the same for every member of the co-phased prescribed-velocity family; at $m=2$ the physical Eulerian mean peaks an order of magnitude above $ψ_2$, with opposite sign. The no-slip cell centers lie at $r^2 = m/(m+2)$, and at large $m$ the peak streamfunction falls as $m^{-2}$, the peak speed as $m^{-1}$. At fixed radial wall-velocity amplitude the ranking over $m$ follows the wall kinematics: an externally driven wall peaks at $m=1$, a wall with zero first-order surface strain at $m=3$. Mode superpositions invert without degenerating, each harmonic carrying its own correction. At finite $\\mathrm{Wo}$ the first-order field stays closed form in Bessel functions and the mean flow reduces to quadrature; the construction approaches the $m=2$ Rayleigh limit on a separate tangentially driven boundary problem. An independent finite-element solver, with the closed form withheld, reproduces $ψ_2$ with quadratic mesh convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24368",
  "author_total": 6,
  "authors": [
    {
      "name": "Zijian Liu"
    },
    {
      "name": "Julian Olszewski"
    },
    {
      "name": "Yang Lin"
    },
    {
      "name": "Yuan Gao"
    },
    {
      "name": "Mengren Wu"
    },
    {
      "name": "Jie Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddnagfq9ktcsd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24368",
  "fulltext_url": null,
  "id": "ddnagfq9ktcsd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24368",
  "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": "W7214020066",
  "pdf_url": "https://arxiv.org/pdf/2609.24368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddnagfq9ktcsd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.24368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24368"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A closed-form solution for streaming and Lagrangian transport in a deforming circular cavity",
  "title_text": "A closed-form solution for streaming and Lagrangian transport in a deforming circular cavity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/ddnagfq9ktcsd",
  "venue": "arXiv",
  "versions": []
}