{
  "id": "2207.06808",
  "version": "v1",
  "published": "2022-07-14T10:37:10.000Z",
  "updated": "2022-07-14T10:37:10.000Z",
  "title": "Reduced-order Galerkin models of plane Couette flow",
  "authors": [
    "André V. G. Cavalieri",
    "Petrônio A. S. Nogueira"
  ],
  "comment": "10 pages, 4 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without sign of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-14T10:37:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane couette flow",
      "reduced-order galerkin models",
      "galerkin systems comprise ordinary differential",
      "systems comprise ordinary differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}