River channel networks created by Poisson Equation and Inhomogeneous Permeability Models
River channel networks created by Poisson Equation and Inhomogeneous Permeability Models
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由泊松方程和非均匀渗透率模型创建的河道网络
DOI：
10.15748/jasse.4.176
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Hiroshi Serizawa
中科院分区：
文献类型：
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作者：
Hiroshi Serizawa
． 本文提出了原始的数学模型来模拟树突树网络的形成，如天然河道。这些分别被称为泊松方程模型（PEM）和非均匀渗透率模型（IPM），其中二维泊松方程在齐次或非齐次条件下求解。特别重要的是IPM，它假设渗透率随地点而变化，这反映了土壤、降水等地理特性的区域波动。最优河道网络（OCN）理论或构律认为，天然河流流域应该实现一种总能量消耗或流阻最小的优化原则。从最优化的角度出发，利用PEMs和IPMs对区域到点流系统的可能结构进行了探讨。根据数值模拟，我们认为自然河流景观的分形结构的起源是地貌条件的异质性。该研究表明，渗透率随机化方法不仅可以作为一种实用的工具，而且可以作为一种有指导意义的工具来重现自然扰动的河网系统。
. This paper presents original mathematical models to simulate formation of dendritic tree networks such as natural river channels. These are referred to as the Poisson Equation Model (PEM) and as the Inhomogeneous Permeability Model (IPM), respectively, where the two-dimensional Poisson equations are solved under the homogeneous or the inhomogeneous condition. Particularly important is the IPM, which assumes that permeability varies depending on the site, which reflects regional fluctuations of geographical properties such as soil, precipitation, and so on. Natural river basins are supposed to realize a kind of optimization principle such that total energy expenditure or flow resistance is minimal, as stated by the Optimal Channel Network (OCN) theory or the Constructal law. From a viewpoint of optimization, possible structures of area-to-point flow systems are explored by use of PEMs and IPMs. According to our numerical simulations, it is supposed that the origin of the fractal structure that characterizes natural fluvial landscapes is heterogeneity in geomorphic conditions. This study indicates that the permeability randomization method can be utilized not only as a practical but also as an instructive tool to reproduce naturally disturbed river network systems.