一个用于描述非饱和介质中水分运移的非玻尔兹曼尺度的分形理查兹方程。
A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media.
作者信息
Sun Hongguang, Meerschaert Mark M, Zhang Yong, Zhu Jianting, Chen Wen
机构信息
College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China.
出版信息
Adv Water Resour. 2013 Feb 1;52:292-295. doi: 10.1016/j.advwatres.2012.11.005.
The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature.
传统的理查兹方程表明，非饱和土壤中的湿润锋遵循玻尔兹曼标度律，运移距离随时间的平方根增长。本研究提出了一个分形理查兹方程（FRE），用分形导数代替含水量的整数阶时间导数，采用时间上的幂律尺度。FRE解表现出异常的非玻尔兹曼标度，这归因于非均质介质的分形性质。给出了几个应用实例，将FRE拟合到先前文献中的含水量曲线。
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