Repository: Freie Universität Berlin, Math Department

Multiscale analyses for the Shallow Water equations

Bresch, D. and Klein, R. and Lucas, C. (2011) Multiscale analyses for the Shallow Water equations. Computational Science and High Performance Computing IV, 115/20 . pp. 149-164. ISSN 1612-2909 (Print) 1060-0824 (Online)


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This paper explores several asymptotic limit regimes for shallow water flows over multiscale topography. Depending on the length and time scales considered and on the characteristic water depth and height of topography, a variety of mathematically quite different asymptotic limit systems emerges. Specifically, we recover the classical “lake equations” for balanced flow without gravity waves in the single time, single space scale limit (Greenspan, Cambridge Univ. Press, (1968)), discuss a weakly nonlinear and a strongly nonlinear multi-scale version of these wave-free equations involving short-range topography, and we re-derive the equations for long-wave shallow water waves passing over short-range topography by Le Maître et al., JCP (2001)

Item Type:Article
Additional Information:The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, October 12 to 16, 2009
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:687
Deposited By: Ulrike Eickers
Deposited On:03 Aug 2009 08:35
Last Modified:03 Mar 2017 14:40

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