23 Aug 2022
23 Aug 2022
Status: this preprint is open for discussion.

Semi-continuum modelling of unsaturated porous media flow to explain the Bauters' paradox

Jakub Kmec1, Miloslav Šír1, Tomáš Fürst2, and Rostislav Vodák2 Jakub Kmec et al.
  • 1Palacký University in Olomouc, Joint Laboratory of Optics of Palacky University and Institute of Physics of the Academy of Sciences of the Czech Republic, Faculty of Science, Olomouc, 771 46, Czech Republic
  • 2Palacký University in Olomouc, Dpt. Mathematical Analysis and Applications of Mathematics, Faculty of Science, Olomouc, 771 46, Czech Republic

Abstract. In gravity-driven free infiltration of a wetting liquid into a homogeneous unsaturated porous medium, the flow pattern is known to depend significantly on the initial saturation. Point-source infiltration of a liquid into an initially dry porous medium produces a single finger with an oversaturated tip and an undersaturated tail. In an initially wet medium, a diffusion-like plume is produced with a monotonic saturation profile. We present a semi-continuum model based on a proper scaling of the retention curve which is discrete in space and continuous in time. We show that the semi-continuum model is able to describe this transition and to capture the experimentally observed dependence of the saturation overshoot and the finger velocity on the initial saturation.

Jakub Kmec et al.

Status: open (until 19 Oct 2022)

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  • RC1: 'Comment on egusphere-2022-673', Anonymous Referee #1, 04 Oct 2022 reply

Jakub Kmec et al.

Data sets

Simulation data for: Semi-continuum modelling of unsaturated porous media flow to explain the Bauters' paradox Jakub Kmec, Miloslav Šír, Tomáš Fürst, Rostislav Vodák

Model code and software

The semi-continuum model for unsaturated porous media flow Jakub Kmec

Jakub Kmec et al.


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Short summary
When rain falls on the ground, most of the water subsequently flows through the soil. The movement of water through the partially wet soil layer is surprisingly complicated. For decades, no mathematical model has been able to capture this process in its entire complexity. Here, we present a model that aims to solve this long-standing problem. In this paper, we show that the model correctly reproduces the transition between diffusion and preferential flow regimes.