{
  "id": "2304.11545",
  "version": "v1",
  "published": "2023-04-23T05:36:25.000Z",
  "updated": "2023-04-23T05:36:25.000Z",
  "title": "Monotone energy stability for Poiseuille flow in a porous medium",
  "authors": [
    "Giuseppe Mulone"
  ],
  "comment": "9 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the monotone energy stability of ``Poiseuille flow\" in a plane-parallel channel with a saturated porous medium modeled by the Brinkman equation, on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow) (cf. \\cite{Hill.Straughan.2010}, \\cite{Nield.2003}). We prove that the least stabilizing perturbations, in the energy norm, are the two-dimensional spanwise perturbations. This result implies a Squire theorem for monotone nonlinear energy stability. Moreover, for Reynolds numbers less than the critical Reynolds number $R_E $ there can be no transient energy growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-23T05:36:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76E05",
      "76S05"
    ],
    "keywords": [
      "monotone energy stability",
      "poiseuille flow",
      "porous medium",
      "monotone nonlinear energy stability",
      "transient energy growth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}