Jurcisinová E, Jurcisin M
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Kosice, Slovakia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1 Pt 2):016306. doi: 10.1103/PhysRevE.77.016306. Epub 2008 Jan 22.
The influence of uniaxial small-scale anisotropy on the stability of the scaling regimes and on the anomalous scaling of the structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator product expansion within one-loop approximation. Possible scaling regimes are found and classified in the plane of exponents epsilon-eta , where epsilon characterizes the energy spectrum of the velocity field in the inertial range E proportional, variantk;{1-2epsilon} , and eta is related to the correlation time of the velocity field at the wave number k which is scaled as k;{-2+eta} . It is shown that the presence of anisotropy does not disturb the stability of the infrared fixed points of the renormalization group equations, which are directly related to the corresponding scaling regimes. The influence of anisotropy on the anomalous scaling of the structure functions of the passive scalar field is studied as a function of the fixed point value of the parameter u , which represents the ratio of turnover time of scalar field and velocity correlation time. It is shown that the corresponding one-loop anomalous dimensions, which are the same (universal) for all particular models with a concrete value of u in the isotropic case, are different (nonuniversal) in the case with the presence of small-scale anisotropy and they are continuous functions of the anisotropy parameters, as well as the parameter u . The dependence of the anomalous dimensions on the anisotropy parameters of two special limits of the general model, namely, the rapid-change model and the frozen velocity field model, are found when u-->infinity and u-->0 , respectively.
通过场论重整化群和单圈近似下的算符乘积展开，研究了单轴小尺度各向异性对具有有限关联时间的高斯螺线管速度场平流的被动标量的标度律稳定性和结构函数反常标度的影响。在指数ε-η平面上找到了可能的标度律并进行了分类，其中ε表征惯性范围内速度场的能谱(E\propto k^{1 - 2\varepsilon})，η与波数(k)处速度场的关联时间有关，其标度为(k^{-2 + \eta})。结果表明，各向异性的存在并不干扰重整化群方程红外不动点的稳定性，这些不动点与相应的标度律直接相关。研究了各向异性对被动标量场结构函数反常标度的影响，它是参数(u)的不动点值的函数，(u)表示标量场周转时间与速度关联时间的比值。结果表明，在各向同性情况下，对于具有具体(u)值的所有特定模型，相应的单圈反常维数是相同的（普适的）；而在存在小尺度各向异性的情况下，它们是不同的（非普适的），并且是各向异性参数以及参数(u)的连续函数。分别在(u\to\infty)和(u\to{0})时，找到了一般模型的两个特殊极限，即快速变化模型和冻结速度场模型的反常维数对各向异性参数的依赖关系。
