Practical formulation for finger flow is lacking even though such a non-Darcy flow is commonly observed in homogeneous snow porous media. This study generalized physics for porous media flow based on the Lagrangian Mechanics; for instance, Darcy formula was theoretically derived minimizing the energy loss by solving the Euler-Lagrange Equation with Rayleigh dissipation function. This least energy loss (LEL) principle was then used to elucidate the finger flow formation in homogenous media. It was found that the inactive saturation (non-contributing void fraction) plays an important role in finger flow formation. This new theory also linked Darcy-Richards capillary flow and Newtonian viscous flow theories. Predicted flow area fractions by the LEL model were verified by the cold room laboratory experiment using well-controlled, homogeneous snow sample, as performed and documented by Katsushima et al. (2013).

尽管在均匀的雪多孔介质中经常观察到这种非达西流，但仍缺乏指状流的实用公式。本研究基于拉格朗日力学推广了多孔介质流动物理学；例如，达西公式是通过用瑞利耗散函数求解欧拉-拉格朗日方程，从理论上推导出最小化能量损失的。这种最小能量损失（LEL）原理随后被用来阐明均质介质中指状流的形成。研究发现，非活性饱和度（无贡献的空隙率）在指状流形成中起着重要作用。这一新理论还将达西-理查兹毛细管流和牛顿粘性流理论联系起来。LEL 模型预测的流动面积分数通过冷室实验室实验使用控制良好的均匀雪样进行验证，由 Katsushima 等人进行和记录。（2013）。