{
  "id": "2209.10511",
  "version": "v1",
  "published": "2022-09-21T17:18:36.000Z",
  "updated": "2022-09-21T17:18:36.000Z",
  "title": "Exact Coherent Structures in Fully Developed Two-Dimensional Turbulence",
  "authors": [
    "Dmitriy Zhigunov",
    "Roman O. Grigoriev"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which distinguish them from analogous solutions of the Navier-Stokes equation describing transitional flows. First of all, they come in high-dimensional continuous families. Second, solutions of different types are connected, e.g., an equilibrium can be smoothly continued to a traveling wave or a time-periodic state. Third, and most important, many of these solutions are dynamically relevant for turbulent flow at high Reynolds numbers. Specifically, we find that turbulence in numerical simulations exhibits large-scale coherent structures resembling some of our time-periodic solutions both frequently and over long temporal intervals. Such solutions are analogous to exact coherent structures originally introduced in the context of transitional flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-21T17:18:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact coherent structures",
      "fully developed two-dimensional turbulence",
      "transitional flows",
      "periodic boundary conditions",
      "high reynolds numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}