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A free-boundary model of diffusive valley growth: theory and observation.

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.

SUBMITTER: Yi R

PROVIDER: S-EPMC5493952 | biostudies-literature | 2017 Jun

REPOSITORIES: biostudies-literature

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A free-boundary model of diffusive valley growth: theory and observation.

Yi Robert R Cohen Yossi Y Seybold Hansjörg H Stansifer Eric E McDonald Robb R Mineev-Weinstein Mark M Rothman Daniel H DH

Proceedings. Mathematical, physical, and engineering sciences 20170621 2202

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 slow ...[more]

PMID: 28690414

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