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Mathematical Analysis of a Model of River Channel Formation

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Díaz Díaz, Jesús Ildefonso and Fowler, A.C. and Muñoz, Ana Isabel and Schiavi, E. (2008) Mathematical Analysis of a Model of River Channel Formation. Pure and Applied Geophysics, 165 (8). pp. 1663-1682. ISSN 0033-4553

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Official URL: http://www.springerlink.com/content/k130385n2109476k/


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Abstract

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin.


Item Type:Article
Uncontrolled Keywords:drainage-basin evolution; driven theory; stability; inception; equation; river models; landscape evolution; nonlinear parabolic equations; free boundaries; singular free boundary flux
Subjects:Sciences > Mathematics > Differential equations
ID Code:15177
Deposited On:10 May 2012 08:28
Last Modified:12 Dec 2018 15:07

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