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Comptes Rendus Mathématique
Volume 343, n° 7
pages 499-504 (octobre 2006)
Doi : 10.1016/j.crma.2006.09.016
Received : 12 June 2006 ;  accepted : 5 September 2006
Linear theory of wave generation by a moving bottom
Théorie linéaire de génération de vagues par mouvement du fond
 

Denys Dutykh a , Frédéric Dias a , Youen Kervella b
a Centre de mathématiques et de leurs applications, École normale supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan cedex, France 
b Université de Bretagne Occidentale, 6, avenue Le Gorgeu, 29200 Brest, France 

Abstract

The computation of long wave propagation through the ocean obviously depends on the initial condition. When the waves are generated by a moving bottom, a traditional approach consists in translating the frozen' sea bed deformation to the free surface and propagating it. The present study shows the differences between the classical approach (passive generation) and the active generation where the bottom motion is included. The analytical solutions presented here exhibit some of the drawbacks of passive generation. The linearized solutions seem to be sufficient to consider the generation of water waves by a moving bottom. To cite this article: D. Dutykh et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Résumé

Les calculs de propagation dʼondes longues à travers lʼocéan doivent naturellement être alimentés par la condition initiale. Le but de cette note est de montrer lʼinsuffisance de lʼapproche classique qui consiste à translater la déformation « gelée » du fond vers la surface libre et à la laisser se propager. Un calcul analytique qui met en évidence les inconvénients de lʼapproche classique de génération passive est présenté ici. Les solutions linéarisées semblent être bien adaptées pour traiter la génération de vagues par mouvement du fond. Pour citer cet article : D. Dutykh et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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