Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary angles

Nikolay Kuznetsov

doi:10.1016/j.crme.2003.10.008

Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary angles

Presented by: Évariste Sanchez-Palencia

Nikolay Kuznetsov ¹

¹ Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russian Federation

Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 73-78.

Abstract
Résumé

This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements.

Cette Note porte sur un problème linéarisée du mouvement sur la houle d'un cylindre flottant dans une mer de profondeur infinie. L'unicité du problème est démontrée pour toutes les valeurs de la fréquence d'ondes si la forme du cylindre qui peut intersecter la surface libre sous d'angles arbitraires satisfait á des certaines conditions géométriques.

Received: 2003-10-16
Accepted: 2003-10-28
Published online: 2003-12-18

DOI: 10.1016/j.crme.2003.10.008

Keywords: Fluid mechanics, Water waves, Floating cylinder, Conformal mapping, Integral identity, Uniqueness theorem
Mots-clés : Mécanique des fluides, Ondes de surface, Cylindre flottant, Transformation conforme, Identité intégrale, Théorème d'unicité

Author's affiliations:

Nikolay Kuznetsov ¹

¹ Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russian Federation

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Nikolay Kuznetsov. Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary angles. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 73-78. doi : 10.1016/j.crme.2003.10.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.10.008/

References
Cited by

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[4] M. McIver An example of non-uniqueness in the two-dimensional linear water-wave problem, J. Fluid Mech., Volume 315 (1996), pp. 257-266

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[9] M. McIver Uniqueness and trapped modes for a symmetric structure, Proc. of the 14th Int. Workshop on Water Waves and Floating Bodies, University of Michigan, Ann Arbor, 1999

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