Yi, R;
Cohen, Y;
Seybold, H;
Stansifer, E;
McDonald, NR;
Mineev-Weinstein, M;
Rothman, D;
(2017)
A free-boundary model of diffusive valley growth: theory and observation.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
, 473
(2202)
, Article 20170159. 10.1098/rspa.2017.0159.
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Abstract
Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through linearly diffusive erosion, and we obtain a solution for the valley shape in three dimensions. Our solution compares well to the shape of slowly growing groundwater-fed valleys found in Bristol, Florida. Our results identify a new feature in the formation of groundwater-fed valleys: a spatially variable diffusivity that can be modelled by a fixed-height moving boundary.
| Type: | Article |
|---|---|
| Title: | A free-boundary model of diffusive valley growth: theory and observation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1098/rspa.2017.0159 |
| Publisher version: | http://dx.doi.org/10.1098/rspa.2017.0159 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | moving-boundary problem, valley growth, erosion |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1559918 |
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