TY - JOUR

T1 - The renormalization group in the problem of turbulent convection of a passive scalar impurity with nonlinear diffusion

AU - Antonov, N. V.

N1 - Funding Information: I am grateful to L. Ts. Adzhemyan, A. N. Vasil’ev, M. Gnatich, and D. Horvath for useful discussions. The work was supported financially by the Russian Fund for Fundamental Research (Grant No. 96-02-17-033) and the Grant Center of Natural Sciences of the State Committee of Institutions of Higher Learning (Grant No. 95-0-5.1-30).

PY - 1997/11

Y1 - 1997/11

N2 - The problem of turbulent mixing of a passive scalar impurity is studied within the renormalization-group approach to the stochastic theory of developed turbulence for the case where the diffusion coefficient is an arbitrary function of the impurity concentration. Such a problem incorporates an infinite number of coupling constants ("charges"). A one-loop calculation shows that in the infinite-dimensional space of the charges there is a two-dimensional surface of fixed points of the renormalization-group equations. When the surface has an IR-stability region, the problem has scaling with universal critical dimensionalities, corresponding to the phenomenological laws of Kolmogorov and Richardson, but with nonuniversal (i.e., depending on the Prandtl number and the explicit form of the nonlinearity in the diffusion equation) scaling functions, amplitude factors in the power laws, and value of the "effective Prandtl turbulence number."

AB - The problem of turbulent mixing of a passive scalar impurity is studied within the renormalization-group approach to the stochastic theory of developed turbulence for the case where the diffusion coefficient is an arbitrary function of the impurity concentration. Such a problem incorporates an infinite number of coupling constants ("charges"). A one-loop calculation shows that in the infinite-dimensional space of the charges there is a two-dimensional surface of fixed points of the renormalization-group equations. When the surface has an IR-stability region, the problem has scaling with universal critical dimensionalities, corresponding to the phenomenological laws of Kolmogorov and Richardson, but with nonuniversal (i.e., depending on the Prandtl number and the explicit form of the nonlinearity in the diffusion equation) scaling functions, amplitude factors in the power laws, and value of the "effective Prandtl turbulence number."

UR - http://www.scopus.com/inward/record.url?scp=33749990127&partnerID=8YFLogxK

U2 - 10.1134/1.558427

DO - 10.1134/1.558427

M3 - Article

AN - SCOPUS:33749990127

VL - 85

SP - 898

EP - 906

JO - Journal of Experimental and Theoretical Physics

JF - Journal of Experimental and Theoretical Physics

SN - 1063-7761

IS - 5

ER -