{
  "id": "1202.4588",
  "version": "v2",
  "published": "2012-02-21T10:32:23.000Z",
  "updated": "2012-06-20T15:43:39.000Z",
  "title": "A non-perturbative renormalization group study of the stochastic Navier--Stokes equation",
  "authors": [
    "Carlos Mejía-Monasterio",
    "Paolo Muratore-Ginanneschi"
  ],
  "comment": "RevTeX, 18 pages, 5 figures. Minor changes and new discussions",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the renormalization group flow of the average action of the stochastic Navier--Stokes equation with power-law forcing. Using Galilean invariance we introduce a non-perturbative approximation adapted to the zero frequency sector of the theory in the parametric range of the H\\\"older exponent $4-2\\,\\varepsilon$ of the forcing where real-space local interactions are relevant. In any spatial dimension $d$, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for $\\varepsilon=2$ as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a \\emph{saturation} in the $\\varepsilon$-dependence of the scaling dimension of the eddy diffusivity at $\\varepsilon=3/2$ when, according to perturbative renormalization, the velocity field becomes infra-red relevant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-20T15:43:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47.27.ef",
      "05.10.Cc"
    ],
    "keywords": [
      "stochastic navier-stokes equation",
      "non-perturbative renormalization group study",
      "kinetic energy spectrum",
      "resulting renormalization group flow",
      "real-space local interactions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.86.016315",
      "journal": "Physical Review E",
      "year": 2012,
      "month": "Jul",
      "volume": 86,
      "number": 1,
      "pages": "016315"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhRvE..86a6315M"
    }
  }
}