{
  "abstract": "The main hypothesis of this paper is that inertial effects known from porous-media flow can be observed even in a simple system consisting of a single channel. The strength of inertia is controlled by the Reynolds number, $Re$. We investigated fluid flow through a channel with a cavity in the shape of a Koch leaf. The Koch leaf of level-6 was chosen because it combines regularity, repeatability, and representativeness with a complex multiscale structure and non-trivial hydrodynamic interactions. We analyzed nonlinear effects through the so-called friction factor and show that its deviation from Darcy's law is very subtle. We further examined the influence of inertia on the flow structure, including the participation number $π$ and the backward-flow fraction $ρ^{-}$. In contrast to disordered porous media, the participation number decreases with $Re$, indicating that inertia concentrates kinetic energy in the main through-flow, while recirculation (backward flow) increasingly occupies the Koch leaf cavity. The tortuosity varies non-monotonically with $Re$, the apparent permeability decreases, and in the inertial regime the two are related by a power law with an exponent comparable to that found for natural rock. At the lowest and highest Reynolds numbers, the local kinetic energy followed a power-law distribution, $P(\\varepsilon)\\propto\\varepsilon^{-m}$, over several orders of magnitude with the same exponent, $m\\approx0.83$; inertia modified only the tails of the distribution. Our research can be regarded as an investigation of transport in an extremely porous system with porosity $φ\\approx 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38493",
  "author_total": 4,
  "authors": [
    {
      "name": "Sahrish B. Naqvi"
    },
    {
      "name": "Dawid Strzelczyk"
    },
    {
      "name": "Maciej Tadej"
    },
    {
      "name": "Maciej Matyka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjz4d7va38dqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38493",
  "fulltext_url": null,
  "id": "cjz4d7va38dqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38493",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjz4d7va38dqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38493"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Inertial flows over the Koch leaf",
  "title_text": "Inertial flows over the Koch leaf",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/cjz4d7va38dqr",
  "venue": "arXiv",
  "versions": []
}