FURTHER ANALYSIS OF OPTIMAL MEAN SQUARE ESTIMATION AND NONLINEAR IEM MODEL
最小均方差条件和非线性IEM模型的分析

In this paper the implication of the Optimal Mean Square Estimation (OMSE) condition on the mixing model is further discussed. It is proved that the OMSE condition can replace the moment equations as the constraints facilitating the modeling of mixing term, and that an exact expansion of the mixing term can be deduced by solely using OMSE condition, which is proved consistent with the exact results of Valino et al. in the long relaxation time limit. The nonlinear IEM (NLIEM) model is deduced as a result of a general formula. Finally, two basic flow fields are calculated with NLIEM model, the first of which is the binary mixing of an passive scalar in a homogeneous stationary velocity field and the second is the evolution of passive temperature fluctuation in a grid turbulence with a constant mean transverse temperature gradient imposed. The results are compared with those calculated with IEM model based on the DNS and experimental data. It is found that in the first problem the initial relaxation of the PDF observed in the DNS data is accurately predicted with NLIEM model but very bad with IEM, although both of them predict correctly the final relaxation to Gaussian PDF. In the second problem, the exponential tails observed in the PDF's of temperature fluctuation are reproduced more notably with NLIEM than IEM model and the super flatness of the PDF predicted with NLIEM model relaxes to around 18 which is more close to the experimental value 20 than 15, the value predicted with IEM model.