A study on tubulence models for diffusion and absorption of contaminant and carbon dioxide within vegetation

在本研究中，我们提出了两种植被内污染物和二氧化碳扩散和吸收的湍流模型。一种是（k-ε）型模型，另一种是LES（大涡模拟）模型。在（k-ε）模型中，我们采用先取集合函数，再取基本方程的空间平均的方法。对空间平均值采用滤波处理。我们假设领带过滤器足够光滑，尽管它是大礼帽类型的。由压力和应变引起的阻力通过取集合平均Navier-Stokes方程解析得到。在此基础上推导了紊流能量和粘性耗散率的方程。建立了植被对湍流能量和粘性耗散率方程的影响模型，并对方程进行了封闭处理，将模型计算结果与实测数据进行了对比验证。对于LES模型，我们采用了足够光滑的顶帽滤波。虽然通常使用smagorinsky型LES模型，但我们采用的是单方程LES模型。因为出现在亚网格尺度湍流方程中的尾迹产生项是不可忽略的。通过与实测数据的比较，验证了单方程LES模型的有效性。

In this study, we proposed two kinds of turbulence models for diffusion and absarption oficontamioant and carbon dioxide within vegetation. One (k-ε) type model and the other is a LES(Large Eddy Simulation) model. In cam of (k-ε) model, we adopt the procedure where we took the ensemble avenges and then the spatial averages of the basic equations. A filter was adopted for the spatial average. We assumed that tie filter was sufficiently smooth, though it was top-hat type. The drag force due to pressure and strain was analytically derived from taking the ensemble-averaged Navier-Stokes equation. Moreover, the equations of turbulent energy and viscous dissipation rate were derived from the basic equations. The effects of vegetation on the equations of turbulent energy and viscous dissipation rate were modeled and the equations were closed The validation was tried by comparing the results from the model with the measured data. In case of LES model, we adopted the sufficiently smooth top-bat filter. Although Smagorinsky-type LES models are usually used, we adopted a one-equation LES model. Because the wake production term which appears in the subgrid-scale turbulence equation is not negligible. The one-equation LES model was validated by comparing the result of the model with the measured data.