4 research outputs found
Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near
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 . 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 , at 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 . The corresponding anomalous exponents are identified with
scaling dimensions of certain composite fields and can be systematically
calculated as series in (the exponent, connected with random force) and
. All calculations are performed in the leading one-loop
approximation.Comment: 11pages, 6 figures, LATEX2e. arXiv admin note: substantial text
overlap with arXiv:1611.00327; text overlap with arXiv:1611.0130