Probability Distribution Function of Passive Scalars in Shell Models

被动分级的问题的一个壳模型版本被介绍，它被 K 的模型启发。Ohkitani 和 M。Yakhot [K。Ohkitani 和 M。Yakhot， Phys。加快。Lett。60 (1988 ) 983；K。Ohkitani 和 M。Yakhot，学监。Theor。Phys。81 (1988 ) 329 ] 。作为处于原来的问题，规定随机的速度地是 Gaussian， δ 及时相关。确定的微分方程被认为是非线性的 Langevin 方程。然后，为被动数量的 PDF 的佛克普朗克常数方程数字地被获得并且解决。在精力输入范围(n 【 5， n 是壳数字) ，被动数量的概率分发功能(PDF ) 在 Gaussian 分发附近。在惯性的范围(5 ≤ n ≤ 16 ) 并且驱散范围(n ≥ 17 ) ，被动数量的概率分发功能(PDF ) 有明显的间歇性。并且被动数量的可伸缩的力量是异常的。数字模拟的结果与试验性的大小相比。

A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 （1988） 329]. As in the original problem, the prescribed random velocity field is Gaussian and 5 correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range （n 〈 5, n is the shell number.）, the probability distribution function （PDF） of passive scalars is near the Gaussian distribution. In inertial range （5≤ n ≤ 16） and dissipation range （n ≥ 17）, the probability distribution function （PDF） of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.