Anomalous scaling in two models of passive scalar advection: Effects of anisotropy and compressibility

被引:33
作者
Antonov, NV
Honkonen, J
机构
[1] St Petersburg State Univ, Dept Theoret Phys, St Petersburg 198904, Russia
[2] Univ Helsinki, Dept Phys, Div Theory, FIN-00014 Helsinki, Finland
来源
PHYSICAL REVIEW E | 2001年 / 63卷 / 03期
关键词
D O I
10.1103/PhysRevE.63.036302
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
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian, delta correlated in time, and scales with a positive exponent epsilon. Explicit inertial-range expressions for the scalar correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal anomalous exponents (dependent only on epsilon and alpha, the compressibility parameter). The complete set of anomalous exponents for the pair correlation functions is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to O(epsilon (2)) using the renormalization group. As in the incompressible case, the exponents exhibit a hierarchy related to the degree of anisotropy: the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. As the degree of compressibility increases, the corrections become closer to the leading terms. The small-scale anisotropy reveals itself in the odd ratios of correlation functions: the skewness factor slowly decreases going down to small scales for the incompressible case, but starts to increase if alpha is large enough. The higher odd dimensionless ratios (hyperskewness, etc.) increase, thus signaling persistent small-scale anisotropy; this effect becomes more pronounced for larger values of alpha.
引用
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页码:363021 / 363027
页数:7
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