{
  "id": "0809.1498",
  "version": "v1",
  "published": "2008-09-09T07:02:51.000Z",
  "updated": "2008-09-09T07:02:51.000Z",
  "title": "The critical layer in pipe flow at high Reynolds number",
  "authors": [
    "D. Viswanath"
  ],
  "doi": "10.1098/rsta.2008.0225",
  "categories": [
    "physics.flu-dyn",
    "physics.plasm-ph"
  ],
  "abstract": "We report the computation of a family of traveling wave solutions of pipe flow up to $Re=75000$. As in all lower-branch solutions, streaks and rolls feature prominently in these solutions. For large $Re$, these solutions develop a critical layer away from the wall. Although the solutions are linearly unstable, the two unstable eigenvalues approach 0 as $Re\\to\\infty$ at rates given by $Re^{-0.41}$ and $Re^{-0.87}$ -- surprisingly, the solutions become more stable as the flow becomes less viscous. The formation of the critical layer and other aspects of the $Re\\to\\infty$ limit could be universal to lower-branch solutions of shear flows. We give implementation details of the GMRES-hookstep and Arnoldi iterations used for computing these solutions and their spectra, while pointing out the new aspects of our method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-09T07:02:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high reynolds number",
      "pipe flow",
      "lower-branch solutions",
      "arnoldi iterations",
      "rolls feature"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Philosophical Transactions of the Royal Society of London Series A",
      "year": 2009,
      "month": "Feb",
      "volume": 367,
      "number": 1888,
      "pages": 561
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009RSPTA.367..561V"
    }
  }
}