TY - JOUR

T1 - Renormalization group, operator expansion, and anomalous scaling in a simple model of turbulent diffusion

AU - Adzhemyan, L. Ts

AU - Antonov, N. V.

AU - Vasil'ev, A. N.

N1 - Funding Information: Acknowledgments. This work was supported in part by the Russian Foundation for Basic Research (Grant No. 99-02-16783) and the Competition Center for Basic Natural Science of the Russian Ministry of Education (Grant No. 97-0-14.1-30).

PY - 1999/8

Y1 - 1999/8

N2 - Using the renormalization group method and the operator expansion in the Obukhov-Kraichnan model that describes the intermixing of a passive scalar admixture by a random Gaussian field of velocities with the correlator 〈v(t, x)v(t′, x)〉 - 〈v(t, x)v(t′, x′)〉 ∝ δ(t - t′)|x - x′|εe, we prove that the anomalous scaling in the inertial interval is caused by the presence of "dangerous" composite operators (powers of the local dissipation rate) whose negative critical dimensions determine the anomalous exponents. These exponents are calculated up to the second order of the ε expansion.

AB - Using the renormalization group method and the operator expansion in the Obukhov-Kraichnan model that describes the intermixing of a passive scalar admixture by a random Gaussian field of velocities with the correlator 〈v(t, x)v(t′, x)〉 - 〈v(t, x)v(t′, x′)〉 ∝ δ(t - t′)|x - x′|εe, we prove that the anomalous scaling in the inertial interval is caused by the presence of "dangerous" composite operators (powers of the local dissipation rate) whose negative critical dimensions determine the anomalous exponents. These exponents are calculated up to the second order of the ε expansion.

UR - http://www.scopus.com/inward/record.url?scp=0033240145&partnerID=8YFLogxK

U2 - 10.1007/BF02557413

DO - 10.1007/BF02557413

M3 - Article

AN - SCOPUS:0033240145

VL - 120

SP - 1074

EP - 1078

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -