| | |
Summary: Shocks in the Evolution of an Eroding Channel
Edward Welsha
, Bj¨orn Birnirb,c,
and Andrea Bertozzid
a Department of Mathematics, Westfield State College, Westfield, MA 01086, USA
b Department of Mathematics, University of California at Santa Barbara, CA 93106, USA
c University of Iceland, Science Institute, 3 Dunhaga, 107 Reykjav´ik, Iceland
d Department of Mathematics, University of California at Los Angeles, CA 90095, USA
August 15, 2006
Abstract
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 un-
stable 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.
1 Introduction
|
