{
  "id": "1005.5517",
  "version": "v1",
  "published": "2010-05-30T11:44:04.000Z",
  "updated": "2010-05-30T11:44:04.000Z",
  "title": "Chaotic dynamics in two-dimensional Rayleigh-Bénard convection",
  "authors": [
    "Supriyo Paul",
    "Mahendra K. Verma",
    "Pankaj Wahi",
    "Sandeep K. Reddy",
    "Krishna Kumar"
  ],
  "comment": "16 pages, 13 figures",
  "categories": [
    "physics.flu-dyn",
    "nlin.CD"
  ],
  "abstract": "We investigate the origin of various convective patterns using bifurcation diagrams that are constructed using direct numerical simulations. We perform two-dimensional pseudospectral simulations for a Prandtl number 6.8 fluid that is confined in a box with aspect ratio $\\Gamma = 2\\sqrt{2}$. Steady convective rolls are born from the conduction state through a pitchfork bifurcation at $r=1$, where $r$ is the reduced Rayleigh number. These fixed points bifurcate successively to time-periodic and quasiperiodic rolls through Hopf and Neimark-Sacker bifurcations at $r \\simeq 80$ and $r \\simeq 500 $ respectively. The system becomes chaotic at $r \\simeq 750$ through a quasiperiodic route to chaos. The size of the chaotic attractor increases at $r \\simeq 840$ through an \"attractor-merging crisis\" which also results in travelling chaotic rolls. We also observe coexistence of stable fixed points and a chaotic attractor for $ 846 \\le r \\le 849$ as a result of a subcritical Hopf bifurcation. Subsequently the chaotic attractor disappears through a \"boundary crisis\" and only stable fixed points remain. Later these fixed points become periodic and chaotic through another set of bifurcations which ultimately leads to turbulence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-30T11:44:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional rayleigh-bénard convection",
      "chaotic dynamics",
      "bifurcation",
      "perform two-dimensional pseudospectral simulations",
      "chaotic attractor increases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5517P"
    }
  }
}