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Correction: Aga, A.O. et al. Estimating the Sediment Flux and Budget for a Data Limited Rift Valley Lake in Ethiopia. Hydrology 2019, 6, 1
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Mathematical Treatment of Saturated Macroscopic Flow in Heterogeneous Porous Medium: Evaluating Darcy’s Law

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Groundwater Hydrologist, Agricultural, and Civil Engineer, Ogden, UT 84401, USA
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Department of Civil and Environmental Engineering, Brigham Young University, 430L EB, Provo, UT 84602, USA
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Author to whom correspondence should be addressed.
Hydrology 2020, 7(1), 4; https://doi.org/10.3390/hydrology7010004
Received: 30 August 2019 / Revised: 26 November 2019 / Accepted: 20 December 2019 / Published: 31 December 2019
We present a rigorous mathematical treatment of water flow in saturated heterogeneous porous media based on the classical Navier-Stokes formulation that includes vorticity in a heterogeneous porous media. We used the mathematical approach proposed in 1855 by James Clark Maxwell. We show that flow in heterogeneous media results in a flow field described by a heterogeneous complex lamellar vector field with rotational flows, compared to the homogeneous lamellar flow field that results from Darcy’s law. This analysis shows that Darcy’s Law does not accurately describe flow in a heterogeneous porous medium and we encourage precise laboratory experiments to determine under what conditions these issues are important. We publish this work to encourage others to perform numerical and laboratory experiments to determine the circumstances in which this derivation is applicable, and in which the complications can be disregarded. View Full-Text
Keywords: porous media; heterogeneous; analytical solution; mathematical treatment; lamellar vector field; rotational flow porous media; heterogeneous; analytical solution; mathematical treatment; lamellar vector field; rotational flow
MDPI and ACS Style

Nelson, R.W.; Williams, G.P. Mathematical Treatment of Saturated Macroscopic Flow in Heterogeneous Porous Medium: Evaluating Darcy’s Law. Hydrology 2020, 7, 4.

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