Whitham's equations for modulated roll-waves in shallow flows

2010/11/10 by Pascal Noble, Noble, Pascal, Luis Miguel Rodrigues +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1011.2296

arxiv created 2010/11/10 · arxiv updated 2010/11/11

Abstract

This paper is concerned with the detailed behaviour of roll-waves undergoing a low-frequency perturbation. We rst derive the so-called Whitham's averaged modulation equations and relate the well-posedness of this set of equations to the spectral stability problem in the small Floquet-number limit. We then fully validate such a system and in particular, we are able to construct solutions to the shallow water equations in the neighbourhood of modulated roll-waves proles that exist for asymptotically large time.

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