Non-uniqueness in two-dimensional water wave problems: Numerical evidence and geometrical restrictions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 453, Issue 1966, 1997, Pages 2437-2460

  Linton, C M ^a   Kuznetsov, N G ^b  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000970797     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1997.0131     Document Type: Article

References (18)

1. Callan, M. A., Linton, C. M. & Evans, D. V. 1991 Trapped modes in two-dimensional waveguides. J. Fluid Mech. 229, 51-64.
2. Evans, D. V. 1970 Diffraction of water waves by a submerged vertical plate. J. Fluid Mech. 40, 433-451.
3. Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261, 21-31.
4. Evans, D. V. & Linton, C. M. 1991 Trapped modes in open channels. J. Fluid Mech. 225, 153-175.
5. Evans, D. V. & Linton, C. M. 1994 Acoustic resonance in ducts. J. Sound Vib. 173, 85-94.
6. John, F. 1950 On the motion of floating bodies. II. Commun. Pure Appl. Math. 3, 45-101.
7. 2u + λu = 0 when the boundary conditions are given on semi-infinite domains. Proc. Camb. Phil. Soc. 49, 668-684.
8. Kuznetsov, N. & Simon, M. J. 1995 On uniqueness in linearized two-dimensional water-wave problems for two surface-piercing bodies. Q. Jl Mech. Appl. Math. 48, 507-515.
9. Kuznetsov, N. G. 1988 Plane problem of the steady-state oscillations of a fluid in the presence of two semiimmersed cylinders. Math. Notes 44, 685-690.
10. Martin, P. A. 1991 End-point behaviour of solutions to hypersingular integral equations. Proc. R. Soc. Lond. A 432, 301-320.
11. Martin, P. A., Parsons, N. F. & Farina, L. 1997 Interaction of water waves with thin plates. In Mathematical techniques for water waves (ed. B. N. Mandal). Advances in Fluid Mechanics Series. Ashurst, Southampton: Computational Mechanics Publications.
12. McIver, M. 1996 An example of non-uniqueness in the two-dimensional linear water wave problem. J. Fluid Mech. 315, 257-266.
13. Parsons, N. F. & Martin, P. A. 1992 Scattering of water waves by submerged plates using hypersingular integral equations. Appl. Ocean Res. 14, 313-321.
14. Parsons, N. F. & Martin, P. A. 1994 Scattering of water waves by submerged curved plates and by surface-piercing flat plates. Appl. Ocean Res. 16, 129-139.
15. Parsons, N. F. & Martin, P. A. 1995 Trapping of water waves by submerged plates using hyper-singular integral equations. J. Fluid Mech., 284, 359-375.
16. Simon, M. J. & Ursell, F. 1984 Uniqueness in linearized two-dimensional water-wave problems. J. Fluid Mech. 148, 137-154.
17. Ursell, F. 1947 The effect of a fixed vertical barrier on surface waves in deep water. Proc. Camb. Phil. Soc. 43, 364-382.
18. Ursell, F. 1992 Some unsolved and unfinished problems in the theory of waves. In Wave asymptotics (ed. P. A. Martin & G. R. Wickham). Cambridge University Press.