{
  "id": "1602.05105",
  "version": "v1",
  "published": "2016-02-16T17:35:29.000Z",
  "updated": "2016-02-16T17:35:29.000Z",
  "title": "Color of turbulence",
  "authors": [
    "Armin Zare",
    "Mihailo R. Jovanović",
    "Tryphon T. Georgiou"
  ],
  "comment": "39 pages, 23 figures",
  "categories": [
    "physics.flu-dyn",
    "math.DS",
    "math.OC",
    "physics.data-an"
  ],
  "abstract": "Second-order statistics of turbulent flows can be obtained either experimentally or via direct numerical simulations. Statistics reflect fundamentals of flow physics and can be used to develop low-complexity turbulence models. Due to experimental or numerical limitations it is often the case that only partial flow statistics can be reliably known, i.e., only certain correlations between a limited number of flow field components are available. Thus, it is of interest to complete the statistical signature of the flow field in a way that is consistent with the known dynamics. This is an inverse problem and our approach utilizes stochastically-forced linearization around turbulent mean velocity profile. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. In contrast, colored-in-time forcing of the linearized equations allows for exact matching of available correlations. To accomplish this, we develop dynamical models that generate the required stochastic excitation and are optimal in a suitable sense (maximum entropy). Generically, these models of the required colored-in-time forcing contain the smallest number of degrees of freedom and, moreover, they can be interpreted as low-rank perturbations of the original linearized NS dynamics. Starting from a limited set of available statistics, the system dynamics impose a linear constraint on the remaining admissible correlations. Completion of the missing correlations is an inverse problem for which we use nuclear norm minimization to obtain correlation structures of low rank. The formulated optimization problem is convex and its globally optimal solution can be efficiently computed. We validate our approach by reproducing statistical features of a turbulent channel flow using stochastic simulations of the modified linearized dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-16T17:35:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "correlation",
      "inverse problem",
      "explain turbulent flow statistics",
      "flow field",
      "original linearized ns dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205105Z"
    }
  }
}