GUILLOPE, Colette; BONA, Jerry; COLIN, Thierry

doi:10.3934/dcds.2013.33.599

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

GUILLOPE, Colette
Laboratoire d'Analyse et de Mathématiques Appliquées [LAMA]

BONA, Jerry
Department of Mathematics, Statistics and Computer Science [Chicago] [UIC]

COLIN, Thierry
Institut de Mathématiques de Bordeaux [IMB]
Modélisation, contrôle et calcul [MC2]

Langue

Article de revue

Ce document a été publié dans

Discrete and Continuous Dynamical Systems - Series A. 2013-02-01, vol. 33, n° 2, p. 599-628

American Institute of Mathematical Sciences

Résumé en anglais

The present essay is concerned with a model for the propagation ofthree-dimensional, surface water waves. Of especial interest will be long-crestedwaves such as those sometimes observed in canals and in near-shore zones oflarge bodies of water. Such waves propagate primarily in one direction, taken tobe the x−direction in a Cartesian framework, and variations in the horizontaldirection orthogonal to the primary direction, the y−direction, say, are oftenignored. However, there are situations where weak variations in the secondaryhorizontal direction need to be taken into account.Our results are developed in the context of Boussinesq models, so they areapplicable to waves that have small amplitude and long wavelength when comparedwith the undisturbed depth. Included in the theory are well-posednessresults on the long, Boussinesq time scale. As mentioned, particular interestis paid to the lateral dynamics, which turn out to satisfy a reduced Boussinesqsystem. Waves corresponding to disturbances which are localized in thex−direction as well as bore-like disturbances that have infinite energy are takenup in the discussion.< Réduire

Mots clés en anglais

Long-crested water waves

Bousinesq system

bore propagation

initial-boundary-value problems

Métadonnées

Licence d’utilisation du document

Propagation of long-crested water waves

Langue

Ce document a été publié dans

Résumé en anglais

Mots clés en anglais

DOI

Origine

Unités de recherche