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The fate of continuous input of relatively heavy fluid at the base of a porous medium

Published online by Cambridge University Press:  02 December 2021

Herbert E. Huppert  and
Samuel S. Pegler Open the ORCID record for Samuel S. Pegler [Opens in a new window]
Herbert E. Huppert*
Affiliation:
Institute of Theoretical Geophysics, King's College, CambridgeCB2 1ST, UK
Samuel S. Pegler
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

We evaluate theoretically and confirm experimentally the shape of the fluid envelope resulting from the input of relatively heavy fluid at a constant rate from a point source at the base of a homogeneous porous medium. In three dimensions an initially expanding hemisphere transitions into a gravity current flowing over the assumed rigid, horizontal and impermeable bottom of the porous medium. A range of increasing transition times occurs if defined by extrapolation of the relationships in the two extreme regimes (hemispherical shape and thin-layer gravity current) so that they intersect, for: the ratio of buoyancy to fluid resistance; the horizontal extent of the fluid; the ratio of height at the centre to the radius; and just the height at the centre. Corresponding results are derived for two-dimensional geometries. In this case, we conduct a series of laboratory experiments demonstrating the transition between the radial and gravity current regimes both in terms of form and propagation rate. The results are extrapolated briefly to two-layer systems, in order to begin to understand effects due to vertically heterogeneous pore structures. We sketch, and verify by experiment, that an expanding hemisphere in a lower layer can reach a much more permeable upper layer and flow through it as a gravity current, thereby uniting the two regimes.

JFM classification

Low-Reynolds-number flows: Porous media Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Hele-Shaw flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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