4 research outputs found
Anomalous exponents in the rapid-change model of the passive scalar advection in the order
Field theoretic renormalization group is applied to the Kraichnan model of a
passive scalar advected by the Gaussian velocity field with the covariance
. Inertial-range
anomalous exponents, related to the scaling dimensions of tensor composite
operators built of the scalar gradients, are calculated to the order
of the expansion. The nature and the convergence of
the expansion in the models of turbulence is are briefly discussed.Comment: 4 pages; REVTeX source with 3 postscript figure
Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order
The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar advected by the Gaussian velocity
field with zero mean and correlation function \propto\delta(t-t')/k^{d+\eps}.
Inertial-range anomalous exponents, identified with the critical dimensions of
various scalar and tensor composite operators constructed of the scalar
gradients, are calculated within the expansion to order
(three-loop approximation), including the exponents in
anisotropic sectors. The main goal of the paper is to give the complete
derivation of this third-order result, and to present and explain in detail the
corresponding calculational techniques. The character and convergence
properties of the expansion are discussed; the improved
``inverse'' expansion is proposed and the comparison with the
existing nonperturbative results is given.Comment: 34 pages, 5 figures, REVTe