{
  "abstract": "A long-standing route to efficient surface-drag prediction in zero-pressure-gradient compressible turbulent boundary layers is to map the skin-friction coefficient $C_f$ and momentum-thickness Reynolds number $Re_θ$ onto their `incompressible' counterparts. Reassessment against an extensive DNS database shows that existing formulations do not consistently recover the reference incompressible skin-friction behaviour, even when transformed data exhibit improved collapse. We define the mapped `incompressible' state as a constant-property counterpart of the physical compressible boundary layer and derive the transformation factors from prescribed mean-velocity and wall-normal-coordinate mappings. This definition-first approach links skin-friction scaling to the full-layer accuracy of the underlying velocity transformation and exposes inherited outer-layer errors. Van Driest's theory is recast in a finite-Re exact-integral form, with the classical vD I and II transformations recovered as leading-order asymptotic reductions. Their limitations at finite Reynolds numbers are quantified, and the historical success of vD II is traced to a fortuitous cancellation of truncation errors. The exact-integral formulation then yields modified transformations assessed through a priori scaling and standalone a posteriori prediction of $C_f$ from prescribed macroscopic and wall-thermal inputs. The VIPL-based modified transformation gives the best overall performance. Across $0.30 \\leq M_\\infty \\leq 13.64$ and $-0.55 \\leq \\varTheta \\leq 2.85$, its prediction errors remain below $11\\%$, with a mean error of $3.07\\%$. Overall, the analysis places skin-friction transformations on a mapping-based exact-integral footing, relating them directly to prescribed mean-flow mappings while avoiding the leading-order asymptotic truncations that limit classical van Driest theory at finite Reynolds numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02650",
  "author_total": 5,
  "authors": [
    {
      "name": "Xuke Zhu"
    },
    {
      "name": "Xiaoshuo Yang"
    },
    {
      "name": "Yongchao Ji"
    },
    {
      "name": "Shiyi Chen"
    },
    {
      "name": "Zhenhua Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/escxckcbp6ns7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02650",
  "fulltext_url": null,
  "id": "escxckcbp6ns7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02650",
  "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": "W7207596401",
  "pdf_url": "https://arxiv.org/pdf/2609.02650",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/escxckcbp6ns7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02650",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02650"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Mapping-based exact-integral formulation of skin-friction transformations for zero-pressure-gradient compressible turbulent boundary layers",
  "title_text": "Mapping-based exact-integral formulation of skin-friction transformations for zero-pressure-gradient compressible turbulent boundary layers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/escxckcbp6ns7",
  "venue": "arXiv",
  "versions": []
}