TY - JOUR

T1 - Exact anomalous dimensions of composite operators in the Obukhov-Kraichnan model

AU - Antonov, N. V.

AU - Gol'din, P. B.

N1 - Funding Information: This work was supported in part by the Nordic Countries Council (Grant No. FIN-20/2003), the prog ram “Universities of Russia,” and the Academy of Finland (Grant No. 203122).

PY - 2004/12

Y1 - 2004/12

N2 - We consider two stochastic equations that describe the turbulent transfer of a passive scalar field θ(x) ≡ θ(t,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 θ(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 θ(x), which allows obtaining exact values for the latter (the values not restricted to the ε-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.

AB - We consider two stochastic equations that describe the turbulent transfer of a passive scalar field θ(x) ≡ θ(t,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 θ(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 θ(x), which allows obtaining exact values for the latter (the values not restricted to the ε-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.

KW - anomalous scaling

KW - Obukhov-Kraichnan model

KW - passive scalar

UR - http://www.scopus.com/inward/record.url?scp=10444233425&partnerID=8YFLogxK

U2 - 10.1023/B:TAMP.0000049764.37693.6d

DO - 10.1023/B:TAMP.0000049764.37693.6d

M3 - Article

AN - SCOPUS:10444233425

VL - 141

SP - 1725

EP - 1736

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -