# Multiscale analyses for the Shallow Water equations: The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, October 12 to 16, 2009

Abstract : 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).
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https://hal.archives-ouvertes.fr/hal-00442344
Contributor : Carine Lucas <>
Submitted on : Sunday, December 20, 2009 - 6:12:22 PM
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Didier Bresch, Rupert Klein, Carine Lucas. Multiscale analyses for the Shallow Water equations: The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, October 12 to 16, 2009. Computational Science and High Performance Computing IV, 115, pp.149-164, 2011, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, ⟨10.1007/978-3-642-17770-5_12⟩. ⟨hal-00442344⟩

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