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Applied Mathematics Research eXpress (2006) Vol. 2006 : article ID 71638, 27 pages, doi:10.1155/AMRX/2006/71638
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Shocks in the evolution of an eroding channel

Edward Welsh, Björn Birnir and Andrea Bertozzi

Department of Mathematics, Westfield State College Westfield, MA 01086, USA E-mail address: ewelsh{at}wsc.ma.edu
Department of Mathematics, University of California Santa Barbara, CA 93106, USA E-mail address: birnir{at}math.ucsb.edu
Department of Mathematics, University of California Los Angeles, CA 90095, USA E-mail address: bertozzi{at}math.ucla.edu

Analysis of an evolution model for a river channel shows how three types of shocks determine the profile of the channel. This model shows that in a young river channel, evolution is driven by a small perturbation magnifying into a bore followed by a hydraulic jump. This mechanism produces a convex profile typical of young landscapes. A small knickpoint then develops at the bottom of the unstable convex profile. This knickpoint evolves into a diffusive shock which travels upslope, digging into the convex profile until the profile becomes concave, typical of mature landscapes.


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