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hal-00534173, version 1

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

Pascal NOBLE 1, Luis Miguel Rodrigues () 1

(2010-11-04)

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.

  • 1:  Institut Camille Jordan (ICJ)
  • CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon
  • Domain : Mathematics/General Mathematics
    Mathematics/Analysis of PDEs
  • Keywords : modulation – wave trains – periodic travelling waves – Saint-Venant equations – Bloch decomposition
 
  • hal-00534173, version 1
  • http://hal.archives-ouvertes.fr/hal-00534173
  • oai:hal.archives-ouvertes.fr:hal-00534173
  • From: Aurélie Reymond <>
  • Submitted on: Tuesday, 9 November 2010 08:41:31
  • Updated on: Tuesday, 16 November 2010 08:02:12