Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d = 4
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 NavierStokes 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 inertialconvective 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 ∊ = 4  d. All calculations are performed in the leading oneloop approximation.
 Publication:

European Physical Journal Web of Conferences
 Pub Date:
 March 2017
 DOI:
 10.1051/epjconf/201713710003
 arXiv:
 arXiv:1611.03708
 Bibcode:
 2017EPJWC.13710003A
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 11pages, 6 figures, LATEX2e. arXiv admin note: substantial text overlap with arXiv:1611.00327