Renormalization group, operator product expansion, and anomalous scaling in a model of advected passive scalar

被引:114
作者
Adzhemyan, LT [1 ]
Antonov, NV [1 ]
Vasil'ev, AN [1 ]
机构
[1] St Petersburg State Univ, Dept Theoret Phys, St Petersburg 198904, Russia
来源
PHYSICAL REVIEW E | 1998年 / 58卷 / 02期
关键词
D O I
10.1103/PhysRevE.58.1823
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Field theoretical renormalization group methods are applied to the Obukhov-Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance [v(t,x)v(t',x)] - [v(t,x)v(t',x')] proportional to delta(t -t')\x-x'\(epsilon). Inertial range anomalous scaling for the structure functions and various pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain essential or ''dangerous'' composite operators [powers of the local dissipation rate], whose negative critical dimensions determine anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order epsilon(2) Of the epsilon expansion. Generalization of the results obtained to the case of a "slow" velocity field is also presented.
引用
收藏
页码:1823 / 1835
页数:13
相关论文
共 48 条
[21]  
Collins J., 1984, RENORMALIZATION, P34, DOI DOI 10.1017/CBO9780511622656
[22]   ENERGY-SPECTRA OF CERTAIN RANDOMLY-STIRRED FLUIDS [J].
DEDOMINICIS, C ;
MARTIN, PC .
PHYSICAL REVIEW A, 1979, 19 (01) :419-422
[23]  
Dominicis CD., 1976, J PHYS-PARIS, V37, P247
[24]   MULTIFRACTALS, OPERATOR PRODUCT EXPANSION, AND FIELD-THEORY [J].
DUPLANTIER, B ;
LUDWIG, AWW .
PHYSICAL REVIEW LETTERS, 1991, 66 (03) :247-251
[25]   Intermittency and anomalous scaling of passive scalars in any space dimension [J].
Eyink, GL .
PHYSICAL REVIEW E, 1996, 54 (02) :1497-1503
[26]   THE RENORMALIZATION-GROUP METHOD IN STATISTICAL HYDRODYNAMICS [J].
EYINK, GL .
PHYSICS OF FLUIDS, 1994, 6 (09) :3063-3078
[27]   Anomalous scaling in a model of passive scalar advection: Exact results [J].
Fairhall, AL ;
Gat, O ;
Lvov, V ;
Procaccia, I .
PHYSICAL REVIEW E, 1996, 53 (04) :3518-3535
[28]   Nonperturbative zero modes in the Kraichnan model for turbulent advection [J].
Gat, O ;
Lvov, VS ;
Podivilov, E ;
Procaccia, I .
PHYSICAL REVIEW E, 1997, 55 (04) :R3836-R3839
[29]  
GAWEDZKI K, 1995, PHYS REV LETT, V75, P3834, DOI 10.1103/PhysRevLett.75.3834
[30]   LAGRANGEAN FOR CLASSICAL FIELD DYNAMICS AND RENORMALIZATION GROUP CALCULATIONS OF DYNAMICAL CRITICAL PROPERTIES [J].
JANSSEN, HK .
ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1976, 23 (04) :377-380