Mejía-Monasterio Carlos, Muratore-Ginanneschi Paolo
Laboratory of Physical Properties, Department of Rural Engineering, Technical University of Madrid, Av. Complutense s/n, 28040 Madrid, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016315. doi: 10.1103/PhysRevE.86.016315. Epub 2012 Jul 16.
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
我们研究了具有幂律强迫的随机纳维-斯托克斯方程平均作用量的重整化群流。利用伽利略不变性，我们引入了一种非微扰近似，该近似适用于理论的零频率扇区，处于强迫的赫尔德指数4 - 2ε的参数范围内，此时实空间局部相互作用是相关的。在任何空间维度d中，我们观察到所得重整化群流收敛到一个唯一的不动点，该不动点产生的动能谱标度与规范维度分析一致。因此，对于ε = 2，恢复了柯尔莫哥洛夫的 -5/3定律，这也是微扰重整化所预测的。与微扰预测不同的是，当根据微扰重整化速度场变为红外相关时，在ε = 3/2处涡扩散率标度维度的ε依赖性存在饱和的情况下出现了 -5/3定律。
