Geodesic
Exact Anomalous Dimensions of Composite Operators in the Obukhov--Kraichnan Model
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 3, pp. 455-468

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We consider two stochastic equations that describe the turbulent transfer of a passive scalar field $\theta(x)\equiv\theta(t,\mathbf x)$ and generalize the known Obukhov–Kraichnan model to the case of a possible compressibility and large-scale anisotropy. The pair correlation function of the field $\theta(x)$ is characterized by an infinite collection of anomalous indices, which have previously been found exactly using the zero-mode method. In the quantum field formulation, these indices are identified with the critical dimensions of an infinite family of tensor composite operators that are quadratic in the field $\theta(x)$, which allows obtaining exact values for the latter (the values not restricted to the $\varepsilon$-expansion) and then using them to find the corresponding renormalization constants. The identification of the correlation function indices with the composite-operator dimensions itself is supported by a direct calculation of the critical dimensions in the one-loop approximation.
Mots-clés : Obukhov–Kraichnan model
Keywords: anomalous scaling, passive scalar. 
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     author = {N. V. Antonov and P. B. Goldin},
     title = {Exact {Anomalous} {Dimensions} of {Composite} {Operators} in the {Obukhov--Kraichnan} {Model}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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N. V. Antonov; P. B. Goldin. Exact Anomalous Dimensions of Composite Operators in the Obukhov--Kraichnan Model. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 3, pp. 455-468. http://geodesic.mathdoc.fr/item/TMF_2004_141_3_a7/