hal-00534173, version 1

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

Pascal NOBLE ¹, Luis Miguel Rodrigues () ¹

(2010-11-04)

• 1:  Institut Camille Jordan (ICJ)
• 
  CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX France

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject:

  Mathematics/General Mathematics

  Mathematics/Analysis of PDEs

• Title: Whitham's equations for modulated roll-waves in shallow flows
• 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.
• Fulltext language: English
• Production date: 2010-11-04
• Keyword(s): modulation – wave trains – periodic travelling waves – Saint-Venant equations – Bloch decomposition
• ANR Project:

  Project Id

  ANR SWECF

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• 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