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The formation of river channels

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Show simple item record Fowler, Andrew C. Kopteva, Natalia Oakley, Charles 2016-04-27T16:07:47Z 2016-04-27T16:07:47Z 2006
dc.identifier.citation Fowler, AC; Kopteva, N; Oakley, C (2006) 'The formation of river channels'. SIAM JOURNAL ON APPLIED MATHEMATICS, 67 :1016-1040. en_US
dc.description peer-reviewed en_US
dc.description.abstract We consider a deterministic model of landscape evolution through the mechanism of overland flow over an erodible substrate, using the St. Venant equations of hydraulics together with the Exner equation for hillslope erosion. A novelty in the model is the allowance for a nonzero bedload layer thickness, which is necessary to distinguish between transport limited and detachment limited sediment removal. It has long been known that transport limited uniform flow is unstable when the hillslope topography is geomorphologically concave (i.e., the center of curvature is above ground). In this paper, we show how finite amplitude development of the consequent channel flow leads to an evolution equation for its depth h of the form h(t) = h(3/2) + (h(3/2))(YY), where Y is the cross-stream space variable. We show that solutions of compact support exist but that, despite appearances, blow up does not occur because of an associated integral constraint, and the channel equation admits a unique and apparently globally stable steady state. The consequences for hillslope evolution models are discussed. en_US
dc.language.iso eng en_US
dc.publisher Society for Industrial and Applied Mathematics en_US
dc.relation.ispartofseries SIAM Journal on Applied Mathematics;67 (4), pp. 1016-1040
dc.rights © 2007 Society for Industrial and Applied Mathematics en_US
dc.subject river networks en_US
dc.subject mathematical geomorphology en_US
dc.subject channel formation en_US
dc.subject nonlinear diffusion en_US
dc.subject drainage-basin evolution en_US
dc.subject elementary theory en_US
dc.subject stability en_US
dc.subject inception en_US
dc.subject model en_US
dc.title The formation of river channels en_US
dc.type info:eu-repo/semantics/article en_US
dc.type.supercollection all_ul_research en_US
dc.type.supercollection ul_published_reviewed en_US 2016-04-27T16:00:39Z
dc.description.version PUBLISHED
dc.rights.accessrights info:eu-repo/semantics/openAccess en_US
dc.internal.rssid 1132414
dc.internal.copyrightchecked Yes
dc.description.status peer-reviewed

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