Communications in Mathematical Sciences

Volume 10 (2012)

Number 3

A two time-scale model for tidal bed-load transport

Pages: 875 – 888



Stéphane Cordier (Bâtiment de mathématiques, Université d’Orléans, France)

Carine Lucas (Bâtiment de mathématiques, Université d’Orléans, France)

Jean De Dieu Zabsonré (ISEA, Université Polytechnique de Bobo-Dioulasso, Burkina Faso)


The aim of this article is to derive a simplified sedimentation model thanks to an asymptotic analysis. We consider a two time scale erosion process due to tidal effects and we show that the approximation at the first order can model bed-load transport well. To this end, the simplified model is validated through numerical tests (evolution of a dune submitted to tidal effects in the ocean, run up near the coast) and compared to direct simulations that are very expensive in terms of computation time.


shallow-water equations, bed-load transport, Exner equation, asymptotic developments, non-dimensional form, limit model, finite volumes scheme

2010 Mathematics Subject Classification

34E13, 65M06, 74S10

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