Analytical Gaussian Solutions for Anisotropie Diffusion in a Linear Shear Flow
Analytical Gaussian Solutions for Anisotropie Diffusion in a Linear Shear Flow
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线性剪切流中各向异性扩散的解析高斯解
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发表时间：
1995
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通讯作者：
P. Konôpka
中科院分区：
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作者：
P. Konôpka
导出了考虑剪切流中物质各向异性输运的扩展扩散方程。空间线性，但随时间变化的流动和沉积速度，随时间变化的扩散张量以及线性汇和源系统的解析解确定。仅考虑空间无限域中的系统，导出了高斯初始分布的解。然后，从这一一般情况出发，推导了水平和线性剪切流的二维和三维解，推广了以往高斯羽流模型的结果。此外，它表明，扩展的扩散方程可以处理的Fokker-Planck方程的解决方案的方法。最后，讨论了如何从这些解的一阶矩和二阶矩确定含时扩散张量。
An extended diffusion equation is derived which takes into account anisotropic transport of mass in a shear flow. Analytical solutions for systems with spatially linear but time-dependent flow and sedimentation velocities, a time-dependent diffusion tensor as well as linear sinks and sources are determined. Considering only systems in spatially infinite domains, the solutions for Gaussian initial distributions are derived. Then, starting from this general case, the twoand three-dimensional solutions are deduced for a horizontal and linear shear flow which generalize the results of former Gaussian plume models. Further, it is shown that the extended diffusion equation can be treated by solution methods of the Fokker-Planck equation. Finally, it is discussed how the time-dependent diffusion tensor can be determined from the first and second moments of these solutions.