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Updated: May 18, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Anomalous scaling of a passive scalar field near two dimensions
A V Gladyshev1, E Jurčišinová, M Jurčišin
1Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141 980 Dubna, Moscow Region, Russian Federation.
Abstract:
The anomalous scaling of the single-time structure functions of a passive scalar field advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and the operator-product expansion with inclusion of additional ultraviolet divergences related to the spatial dimension d=2. Some modification of the standard minimal subtraction scheme is used to calculate the turbulent Prandtl number and the anomalous exponents within the one-loop approximation of a perturbation theory. It is shown that the taking into account of these additional divergences is in full agreement with results obtained in the framework of the usual analytical expansion technique, which are valid for d>2.
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