Uniqueness in the problem of an obstacle in oblique waves

Nikolay Kuznetsov

doi:10.1016/S1631-0721(03)00042-1

Uniqueness in the problem of an obstacle in oblique waves
[Unicité du problème d'un obstacle dans des ondes obliques]

Présenté par : 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, Russia

Comptes Rendus. Mécanique, Volume 331 (2003) no. 3, pp. 183-188.

Résumé
Abstract

Nous considérons le problème du mouvement sur la houle. À partir des conditions géométriques pour deux cylindres flottant dans une mer de profondeur infinie et dans des ondes obliques, nous obtenons un intervalle de fréquences d'unicité.

A solution to the linearized water-wave problem involving a pair of surface-piercing cylinders in oblique waves and infinite water depth is proved to be unique for certain geometric arrangements and frequencies in some interval above the cut-off frequency.

Reçu le : 2003-01-25
Accepté le : 2003-01-25
Publié le : 2003-03-01

DOI : 10.1016/S1631-0721(03)00042-1

Keywords: Fluid mechanics, Oblique waves, Pair of floating cylinders, Nodal line, Conformal mapping, Uniqueness theorem
Mots-clés : Mécanique des fluides, Ondes obliques, Deux cylindres flottants, Courbe nodale, Transformation conforme, Théorème d'unicité

Affiliations des auteurs :

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, Russia

@article{CRMECA_2003__331_3_183_0,
     author = {Nikolay Kuznetsov},
     title = {Uniqueness in the problem of an obstacle in oblique waves},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {183--188},
     publisher = {Elsevier},
     volume = {331},
     number = {3},
     year = {2003},
     doi = {10.1016/S1631-0721(03)00042-1},
     language = {en},
}

TY  - JOUR
AU  - Nikolay Kuznetsov
TI  - Uniqueness in the problem of an obstacle in oblique waves
JO  - Comptes Rendus. Mécanique
PY  - 2003
SP  - 183
EP  - 188
VL  - 331
IS  - 3
PB  - Elsevier
DO  - 10.1016/S1631-0721(03)00042-1
LA  - en
ID  - CRMECA_2003__331_3_183_0
ER  -

%0 Journal Article
%A Nikolay Kuznetsov
%T Uniqueness in the problem of an obstacle in oblique waves
%J Comptes Rendus. Mécanique
%D 2003
%P 183-188
%V 331
%N 3
%I Elsevier
%R 10.1016/S1631-0721(03)00042-1
%G en
%F CRMECA_2003__331_3_183_0

Nikolay Kuznetsov. Uniqueness in the problem of an obstacle in oblique waves. Comptes Rendus. Mécanique, Volume 331 (2003) no. 3, pp. 183-188. doi : 10.1016/S1631-0721(03)00042-1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00042-1/

Bibliographie
Cité par

[1] F. John On the motion of floating bodies. II, Comm. Pure Appl. Math., Volume 3 (1950), pp. 45-101

[2] F. Ursell Surface waves on deep water in the presence of a submerged circular cylinder. I, II, Proc. Cambridge Philos. Soc. (1950), pp. 141-152 (153–158)

[3] F. Rellich Über das asymptotische Verhalten von Δu+λu=0 in unendlichen Gebieten, Jahrsber. Deutsch. Math.-Verein., Volume 53 (1943), pp. 57-65

[4] W.D. Kupradse, Randwertaufgaben der Schwingungstheorie und Integralgleichungen, Deutsch. Verlag Wiss., 1956

[5] N. Kuznetsov; V. Maz'ya; B. Vainberg Linear Water Waves: A Mathematical Approach, Cambridge University Press, 2002

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

[7] N.G. Kuznetsov; R. Porter; D.V. Evans; M.J. Simon Uniqueness and trapped modes for surface-piercing cylinders in oblique waves, J. Fluid Mech., Volume 365 (1998), pp. 351-368

[8] J.N. Newman Radiation and diffraction analysis of the McIver toroid, J. Engrg. Math., Volume 35 (1999), pp. 135-147

[9] F. Ursell Some unsolved and unfinished problems in the theory of waves, Wave Asymptotics, Cambridge University Press, 1992

[10] M. McIver Uniqueness below a cut-off frequency for the two-dimensional linear water-wave problem, Proc. Roy. Soc. London Ser. A, Volume 455 (1999), pp. 1435-1441

[11] F. Ursell The expansion of water-wave potentials at great distances, Proc. Cambridge Philos. Soc., Volume 64 (1968), pp. 811-826

[12] P. Moon; D.E. Spencer Field Theory Handbook, Springer-Verlag, 1971

[13] I.S. Gradshteyn; I.M. Ryzhik Table of Integrals, Series, and Products, Academic Press, 1980

[14] N. Kuznetsov; P. McIver; C.M. Linton On uniqueness and trapped modes in the water-wave problem for vertical barriers, Wave Motion, Volume 33 (2001), pp. 283-307

Cité par Sources :

Commentaires - Politique