A note on stabilizing the Benjamin-Feir instability

Journal of Fluid Mechanics

Volumn 556, Issue , 2006, Pages 45-54

  Wu, Guangyu ^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; DAMPING; FLOW OF FLUIDS; MATHEMATICAL MODELS; WAVEFORM ANALYSIS;

BENJAMIN-FEIR INSTABILITY; NONLINEAR SCHRODINGER EQUATION; STOKES WAVE TRAIN;

FLUID MECHANICS;

COMPUTER SIMULATION; DAMPING; FLOW OF FLUIDS; FLUID MECHANICS; MATHEMATICAL MODELS; WAVEFORM ANALYSIS;

COMPUTER SIMULATION; EQUATION; NONLINEARITY;

EID: 33744917573     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005008293     Document Type: Article

References (15)

1. Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains in deep water. Part 1. Theory. J. Fluid Mech. 27, 417-430.
2. 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.
3. Dommermuth, D. G. & Yue, D. K. P. 1988 The nonlinear three-dimensional waves generated by a moving surface disturbance. In Proc. 17th Symp. on Naval Hydro., The Hague, Netherlands. Washington DC: National Academy Press.
4. Jiang, L., Ting, C.-L., Perlin, M. & Schultz, W. W. 1996 Moderate and steep Farady waves: Instabilities, modulation and temporal asymmetries. J. Fluid Mech. 329, 275-307.
5. Lake, B. M. & Yuen, H. C. 1977 A note on some water-wave experiments and the comparison of data with theory. J. Fluid Mech. 83, 75-81.
6. Lamb, H. 1932 Hydrodynamics, 6th Edn. Cambridge University Press.
7. Liu, Y. & Yue, D. K. P. 1998 On generalized bragg scattering of surface waves by bottom ripples. J. Fluid Mech. 356, 297-326.
8. Lo, E. & Mei, C. C. 1985 numerical study of water-wave modulations based on a higher-order nonlinear schrodinger equation. J. Fluid Mech. 150, 395-416.
9. Longuet-Higgins, M. S. 1997 Viscous dissipation in steep capillary-gravity waves. J. Fluid Mech. 344, 271-289.
10. Mei, C. C. & HancocK, M. J. 2003 Weakly nonlinear surface waves over a random seabed. J. Fluid Mech. 475, 247-268.
11. Ruvinsky, K. D., Feldstein, F. I. & Freidman, G. I. 1991 Numerical simulations of the quasi-stationary stage of ripple excitation by steep-capillary waves. J. Fluid Mech. 230, 339-353.
12. Segur, H., Henderson, D., Carter, J., Hammack, J., Li, C., Pheiff, D., & Socha, K. 2005 Stabilizing the Benjamin-Feir instability. J. Fluid Mech. 539, 229-271 (referred to herein as ℒ).
13. Skandrani, C., Kharif, C. & Poitevin, J. 1996 Nonlinear evolution of water surface waves: The frequency down-shift phenomenon. Contemp. Math. 200, 157-171.
14. Zhang, J., Hong, K. & Yue, D. K. P. 1993 Effects of wavelength ratio on wave-mode modeling. J. Fluid Mech. 248, 107-127.
15. Zhang, W. & Vinals, J. 1997 Pattern formation in weakly damped parametric surface waves. J. Fluid Mech. 336, 301-330.