摘要
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.
基金
The project supported by National Natural Science Foundation for Major Projects under Grant Nos.10336010 and 10576005
