Three-dimensional instability of standing waves

Journal of Fluid Mechanics

Volumn 496, Issue , 2003, Pages 213-242

  Zhu, Qiang ^a   Liu, Yuming ^a   Yue, Dick K P ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; PERTURBATION TECHNIQUES; WAVES;

STANDING WAVES; TRANSITION MATRIX (TM);

FLUID MECHANICS;

FLUID MECHANICS; GRAVITY WAVE; INSTABILITY; MATHEMATICAL MODELING; STANDING WAVE;

EID: 1142281923     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003006347     Document Type: Article

References (43)

1. ABRAMOWITZ, M. & STEGUN, I. A. 1972 Handbook of Mathematical Functions. Dover.
2. BECKER, J. M. & MILES, J. W. 1992 Progressive radial cross-waves. J. Fluid Mech. 245, 29-46.
3. BENDER, C. M. & ORSZAG, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
4. BENJAMIN, T. B. & FEIR, J. E. 1967 The disintegration of wave trains on deep water. 1. Theory. J. Fluid Mech. 27, 417-430.
5. BRIDGES, T. J. 1987 Secondary bifurcation and change of type for three-dimensional standing waves in finite depth. J. Fluid Mech. 179, 137-153.
6. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
7. CODDINGTON, D. A. & LEVINSON, N. 1955 Theory of Ordinary Differential Equations. McGraw-Hill.
8. DOMMERMUTH, D. G. & YUE, D. K. P. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267-288.
9. GOLLUB, J. P. & MEYER, W. 1983 Symmetry-breaking instabilities on a fluid surface. Physica 6D, 337-346.
10. IOUALALEN, M. & KHARIF, C. 1994 On the subharmonic instabilities of steady three-dimensional deep water waves. J. Fluid Mech. 262, 265-291.
11. IOUALALEN, M., ROBERTS, A. J. & KHARIF, C. 1996 On the observability of finite-depth short-crested water waves. J. Fluid Mech. 322, 1-19.
12. JIAN, L., PERLIN, M. & SCHULTZ, W. W. 1998 Period tripling and energy dissipation of breaking standing waves. J. Fluid Mech. 369, 273-299.
13. VON KERCZEK, C. & DAVIS, S. H. 1975 Calculation of transition matrices. AIAA J. 13, 1400-1403.
14. KIMMOUN, O., IOUALALEN, M. & KHARIF, C. 1999 Instabilities of steep short-crested surface waves in deep water. Phys. Fluids 11, 1679-1681.
15. KYOYUL, O. H. & NAYFEH, A. H. 1996 Nonlinear combination resonances in cantilever composite plates. Nonlinear Dyn. 11, 143-169.
16. Liu, Y., DOMMERMUTH, D. G. & YUE, D. K. P. 1992 A high-order spectral method for nonlinear wave-body interactions. J. Fluid Mech. 245, 115-136.
17. Liu, Y. & YUE, D. K. P. 1998 On generalized Bragg scattering of surface waves by bottom ripples. J. Fluid Mech. 356, 297-326.
18. LONGUET-HIGGINS, M. S. 1978a The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics. Proc. R. Soc. Lond. A 360, 471-488.
19. LONGUET-HIGGINS, M. S. 1978b The instabilities of gravity waves of finite amplitude in deep water I. Subharmonics. Proc. R. Soc. Lond. A 360, 489-505.
20. LONGUET-HIGGINS, M. S. & DOMMERMUTH, D. G. 2001 On the breaking of standing waves by falling jets. Phys. Fluids 13, 1652-1659.
21. LONGUET-HIGGINS, M. S. & DRAZEN, D. A. 2002 On steep gravity waves meeting a vertical wall: a triple instability. J. Fluid Mech. 466, 305-318.
22. MACK, L. R. 1962 Periodic, finite-amplitude, axisymmetric gravity waves. J. Geophys. Res. 67, no. 2.
23. McLEAN, J. W. 1982 Instabilities of finite-amplitude water waves. J. Fluid Mech. 114, 315-330.
24. MARTIN, T. 1932 Faraday's Diary, vol. 1, July 5th, 1831 entry. G. Bell.
25. MEI, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. John Wiley.
26. MERCER, G. N. & ROBERTS, A. J. 1992 Standing waves in deep water: their stability and extreme form. Phys. Fluids A 4, 259-269.
27. MILES, J. W. 1984a Resonantly forced surface waves in a circular cylinder. J. Fluid Mech. 149, 15-31.
28. MILES, J. W. 1984b Nonlinear Faraday Resonance. J. Fluid Mech. 146, 285-302.
29. MILES, J. W. 1984c Internally resonant surface waves in a circular cylinder. J. Fluid Mech. 149, 1-14.
30. NAYFEH, A. H. & MOOK, D. T. 1979 Nonlinear Oscillations. John Willey.
31. PHILIPS, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193-217.
32. PIERCE, R. D. & KNOBLOCH, E. 1994 On the modulational stability of traveling and standing water waves. Phys. Fluids 6, 1177-1190.
33. SU, M. Y. 1982 Three-dimensional deep-water waves. Part I. Experimental measurement of skew and symmetric wave patterns. J. Fluid Mech. 124, 73-108.
34. TATSUNO, M., INOUE, S. & OKABE, J. 1969 Transfiguration of surface waves. Rep. Res. Inst. Appl. Mech. Kyushu University 17, 195-215.
35. TSAI, W. T. & YUE, D. K. P. 1987 Numerical calculation of nonlinear axisymmetric standing waves in a circular basin. Phys. Fluids 30, 3441-3447.
36. VANDEN-BROECK, J. M. & SCHWARTZ, L. W. 1981 Phys. Fluids 24, 812.
37. XUE, M., Xu, H., Liu, Y. & YUE, D. K. P. 2001 Computations of fully-nonlinear three-dimensional wave-wave and wave-body interactions. Part 1. Dynamics of three-dimensional steep waves. J. Fluid Mech. 438, 11-39.
38. YUEN, H. C. & FERGUSON, W. E. JR 1978 Relationship between Benjamin-Feir instability and recurrence in the nonlinear Schrödinger equation. Phys. Fluids 21, 1275-1278.
39. YUEN, H. C. & LAKE, B. M. 1980 Instabilities of waves on deep water. Annu. Rev. Fluid Mech. 12, 303-334.
40. ZAKHAROV, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190-194 (English Trans.).
41. ZHANG, J., HONG, K. & YUE, D. K. P. 1993 Effects of wavelength ratio on wave-mode modelling. J. Fluid Mech. 248, 107-127.
42. ZHU, Q. 2000 Features of nonlinear wave-wave and wave-body interactions. PhD thesis, Massachusetts Institute of Technology.
43. ZHU, Q., TJAVARAS, A. A., LIU Y., YUE, D. K. P. & TRIANTAFYLLOU, M. S. 1999 Mechanics of nonlinear short-wave generation by a moored near-surface buoy. J. Fluid Mech. 381, 305-335.