Geodesic
On the problem of time-harmonic water waves in the presence of a~freely-floating structure
Algebra i analiz, Tome 22 (2010) no. 6, pp. 185-199.

Voir la notice de l'article provenant de la source Math-Net.Ru

The two-dimensional problem of time-harmonic water waves in the presence of a freely-floating structure (it consists of a finite number of infinitely long surface-piercing cylinders connected above the water surface) is considered. The coupled spectral boundary value problem modeling the small-amplitude motion of this mechanical system involves the spectral parameter, the frequency of oscillations, which appears in the boundary conditions as well as in the equations governing the structure's motion. It is proved that any value of the frequency turns out to be an eigenvalue of the problem for a particular structure obtained with the help of the so-called inverse procedure.
Keywords: coupled spectral problem, time-harmonic water waves, freely-floating structure, trapped mode. 
@article{AA_2010_22_6_a7,
     author = {N. Kuznetsov},
     title = {On the problem of time-harmonic water waves in the presence of a~freely-floating structure},
     journal = {Algebra i analiz},
     pages = {185--199},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2010_22_6_a7/}
}
TY  - JOUR
AU  - N. Kuznetsov
TI  - On the problem of time-harmonic water waves in the presence of a~freely-floating structure
JO  - Algebra i analiz
PY  - 2010
SP  - 185
EP  - 199
VL  - 22
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2010_22_6_a7/
LA  - en
ID  - AA_2010_22_6_a7
ER  - 
%0 Journal Article
%A N. Kuznetsov
%T On the problem of time-harmonic water waves in the presence of a~freely-floating structure
%J Algebra i analiz
%D 2010
%P 185-199
%V 22
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2010_22_6_a7/
%G en
%F AA_2010_22_6_a7
N. Kuznetsov. On the problem of time-harmonic water waves in the presence of a~freely-floating structure. Algebra i analiz, Tome 22 (2010) no. 6, pp. 185-199. http://geodesic.mathdoc.fr/item/AA_2010_22_6_a7/

[1] John F., “On the motion of floating bodies, I”, Comm. Pure Appl. Math., 2 (1949), 13–57 | DOI | MR | Zbl

[2] Beale J. T., “Eigenfunction expansions for objects floating in an open sea”, Comm. Pure Appl. Math., 30 (1977), 283–313 | DOI | MR | Zbl

[3] John F., “On the motion of floating bodies, II”, Comm. Pure Appl. Math., 3 (1950), 45–101 | DOI | MR

[4] McIver P., McIver M., “Trapped modes in the water-wave problem for a freely floating structure”, J. Fluid Mech., 558 (2006), 53–67 | DOI | MR | Zbl

[5] Fitzgerald C. J., McIver P., “Passive trapped modes in the water wave problem for a floating structure”, J. Fluid Mech., 657 (2010), 456–477 | DOI | Zbl

[6] Kuznetsov N., Maz'ya V., Vainberg B., Linear water waves. A mathematical approach, Cambridge Univ. Press, Cambridge, 2002 | MR

[7] McIver M., “An example of non-uniqueness in the two-dimensional linear water-wave problem”, J. Fluid Mech., 315 (1996), 257–266 | DOI | MR | Zbl

[8] Motygin O., Kuznetsov N., “Non-uniqueness in the water-wave problem: an example violating the inside John condition”, Proceedings of the 13th International Workshop on Water Waves and Floating Bodies, Delft Univ. Technology, 1998, 107–110

[9] Euler L., “Principia motus fluidorum”, Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, VI, 1761, 271–311

[10] Fox D. W., Kuttler J. R., “Sloshing frequencies”, Z. Angew. Math. Phys., 34 (1983), 668–696 | DOI | MR | Zbl

[11] Nazarov S. A., Taskinen Ya., “O spektre zadachi Steklova v oblasti s pikom”, Vestn. S.-Peterburg. un-ta. Ser. 1, 2008, no. 1, 56–65 | Zbl

[12] Appell P. É., Traité de mécanique rationelle, v. 3, Gauthier-Villars, Paris, 1932 | Zbl