Comptes Rendus
Uniqueness in the problem of an obstacle in oblique waves
Comptes Rendus. Mécanique, Volume 331 (2003) no. 3, pp. 183-188.

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.

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.

Published online:
DOI: 10.1016/S1631-0721(03)00042-1
Keywords: Fluid mechanics, Oblique waves, Pair of floating cylinders, Nodal line, Conformal mapping, Uniqueness theorem
Mot clés : Mécanique des fluides, Ondes obliques, Deux cylindres flottants, Courbe nodale, Transformation conforme, Théorème d'unicité

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
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     title = {Uniqueness in the problem of an obstacle in oblique waves},
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     pages = {183--188},
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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.

[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

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