A free-boundary model of diffusive valley growth: theory and observation
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yivalleysub.pdf
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Author(s)
McDonald, Robb
Mineev-Weinstein, Mark
Date Issued
June 2017
Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
Citation
Yi, Robert, Yossi Cohen, Hansjörg Seybold, Eric Stansifer, Robb McDonald, Mark Mineev-Weinstein, and Daniel H. Rothman. “A Free-Boundary Model of Diffusive Valley Growth: Theory and Observation.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 473, no. 2202 (June 2017): 20170159.
Version
Author's final manuscript
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. Keywords: Moving boundary problem, valley growth, erosion
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Lorenz Center (Massachusetts Institute of Technology)
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1098/rspa.2017.0159
