Probability Distribution Function of Passive Scalars in Shell Models

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2008,（4）
• 页码范围: 1033-1038
• 页数: 6页
• 语种: 英文

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 axe 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.