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Active volume of water in a laboratory aquifer

Published online by Cambridge University Press:  27 January 2025

E. Lajeunesse Open the ORCID record for E. Lajeunesse [Opens in a new window] ,
O. Devauchelle Open the ORCID record for O. Devauchelle [Opens in a new window] ,
J. Douçot  and
V. Jules Open the ORCID record for V. Jules [Opens in a new window]
E. Lajeunesse*
Affiliation:
Université Paris Cité, Institut de Physique du Globe de Paris, CNRS, F-75005 Paris, France
O. Devauchelle
Affiliation:
Université Paris Cité, Institut de Physique du Globe de Paris, CNRS, F-75005 Paris, France
J. Douçot
Affiliation:
CY Cergy Paris Université, Laboratoire Géosciences et Environnement Cergy (GEC), 1, rue Descartes, 95000 Neuville-sur-Oise, France
V. Jules
Affiliation:
Institut Pprime, CNRS-Université de Poitiers-ISAE ENSMA, TSA 51124, 86073 Poitiers Cedex 9, France
*
†Email address for correspondence: [email protected]
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Abstract

During a rainfall event, water infiltrates into the ground where it accumulates in porous rocks. This accumulation pushes the underlying groundwater towards neighbouring streams, where it runs to the sea. After the rain has stopped, the aquifer gradually releases its excess water, as the water table relaxes, until the next rain. In the absence of recharge, the water table would eventually reach its horizontal equilibrium position. The volume of groundwater stored above this level, which we call the active volume, sustains the river between two rainfall events. In this article, we use an experimental aquifer recharged by artificial rain to investigate how this active volume depends on the rainfall rate. Restricting our analysis to the steady-state regime, wherein the discharge into the stream balances rainfall, we explore a broad range of rainfall rates, for which the water table deforms significantly. We find that the active volume of water stored in the aquifer decreases with its depth. Using conformal mapping, we derive the flow equations and develop a numerical procedure that accounts for the active volume of groundwater in our experiments. In the case of an infinitely deep aquifer, the problem admits a closed-form solution, which provides a satisfying estimate of the active volume when the aquifer's depth is at least half its width. In the general case, a rougher estimate results from the energy balance of the dissipative groundwater flow.

JFM classification

Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1002 , 10 January 2025 , A36
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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