Xia YuXian, Qian YueHong
Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):023004. doi: 10.1103/PhysRevE.90.023004. Epub 2014 Aug 11.
The direct numerical simulations of forced two-dimensional turbulent flow are presented by using the lattice Boltzmann method. The development of an energy-enstrophy double cascade is investigated in the two cases of external force of two-dimensional turbulence, Gaussian force and Kolmogorov force. It is found that the friction force is a necessary condition of the occurrence of a double cascade. The energy spectrum k(-3) in the enstrophy inertial range is in accord with the classical Kraichnan theory for both external forces. The energy spectrum of the Gaussian force case in an inverse cascade is k(-2); however, the Kolmogorov force drives the k(-5/3) energy in a backscatter cascade. The result agrees with Scott's standpoint, which describes nonrobustness of the two-dimensional turbulent inverse cascade. Also, intermittency is found for the enstrophy cascade in two cases of the external force form. Intermittency refers to the nonuniform distribution of saddle points in the two-dimensional turbulent flow.
采用格子玻尔兹曼方法对二维强迫湍流进行了直接数值模拟。在二维湍流的两种外力情况，即高斯力和柯尔莫哥洛夫力作用下，研究了能量-涡量双级串的发展。发现摩擦力是双级串发生的必要条件。对于两种外力，涡量惯性范围内的能量谱k(-3)都符合经典的克莱奇南理论。高斯力情况下逆级串的能量谱为k(-2)；然而，柯尔莫哥洛夫力在反向散射级串中驱动k(-5/3)能量。该结果与斯科特的观点一致，该观点描述了二维湍流逆级串的非稳健性。此外，在外力形式的两种情况下，涡量级串都存在间歇性。间歇性是指二维湍流中鞍点的非均匀分布。
