{
  "id": "1611.03708",
  "version": "v1",
  "published": "2016-11-11T14:07:41.000Z",
  "updated": "2016-11-11T14:07:41.000Z",
  "title": "Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near $d = 4$",
  "authors": [
    "N. V. Antonov",
    "N. M. Gulitskiy",
    "M. M. Kostenko",
    "T. Lučivjanský"
  ],
  "comment": "11pages, 6 figures, LATEX2e. arXiv admin note: substantial text overlap with arXiv:1611.00327; text overlap with arXiv:1611.01302",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension $d = 4$. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case $d = 3$, at $d = 4$ additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into $d = 3$. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in $y$ (the exponent, connected with random force) and $\\epsilon=4-d$. All calculations are performed in the leading one-loop approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-11T14:07:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "renormalization group analysis",
      "passive scalar field",
      "turbulent compressible fluid",
      "field theoretic renormalization group",
      "random turbulent velocity field"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}