Adzhemyan L T, Antonov N V, Barinov V A, Kabrits Y S, Vasil'ev A N
Department of Theoretical Physics, St. Petersburg University, Uljanovskaja 1, St. Petersburg-Petrodvorez, 198904, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Feb;63(2 Pt 2):025303. doi: 10.1103/PhysRevE.63.025303. Epub 2001 Jan 22.
Field-theoretic renormalization group is applied to the 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('))>~delta(t-t('))|x-x(')|(epsilon). Inertial-range anomalous exponents, related to the scaling dimensions of tensor composite operators built of the scalar gradients, are calculated to the order epsilon(3) of the epsilon expansion. The nature and the convergence of the epsilon expansion in the models of turbulence are briefly discussed.
场论重整化群被应用于由高斯速度场平流的被动标量的克莱奇南模型，其协方差为<v(t,x)v(t('),x)>-<v(t,x)v(t('),x('))>~δ(t - t('))|x - x(')|(ε)。与由标量梯度构成的张量复合算符的标度维数相关的惯性范围反常指数，被计算到ε展开的ε³阶。简要讨论了湍流模型中ε展开的性质和收敛性。
