{
  "id": "2309.03358",
  "version": "v1",
  "published": "2023-09-06T20:50:25.000Z",
  "updated": "2023-09-06T20:50:25.000Z",
  "title": "On a 1/2-equation model of turbulence",
  "authors": [
    "Rui Fang",
    "Weiwei Han",
    "William Layton"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "nlin.CD"
  ],
  "abstract": "In 1-equation URANS models of turbulence the eddy viscosity is given by $\\nu_{T}=0.55l(x,t)\\sqrt{k(x,t)}$ . The length scale $l$ must be pre-specified and $k(x,t)$ is determined by solving a nonlinear partial differential equation. We show that in interesting cases the spacial mean of $k(x,t)$ satisfies a simple ordinary differential equation. Using its solution in $\\nu_{T}$ results in a 1/2-equation model. This model has attractive analytic properties. Further, in comparative tests in 2d and 3d the velocity statistics produced by the 1/2-equation model are comparable to those of the full 1-equation model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-06T20:50:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "turbulence",
      "nonlinear partial differential equation",
      "simple ordinary differential equation",
      "urans models",
      "spacial mean"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}