References
- Bontozoglou , V. and Hanratty , T. J. 1990 . “Capillary-gravity Kelvin-Helmholtz waves close to resonance” . J. Fluid Mech. , 217 : 71 – 91 .
- Brooke Benjamin , T. and Bridges , T. J. 1997a . “Reappraisal of the Kelvin-Helmholtz problem. Part I. Hamiltonian structure” . J. Fluid Mech. , 333 : 301 – 325 .
- Brooke Benjamin , T. and Bridges , T. J. 1997b . “Reappraisal of the Kelvin-Helmholtz problem. Part II. Interaction of the Kelvin-Helmholtz superharmonic and Benjamin-Feir instabilities” . J. Fluid Mech. , 333 : 327 – 373 .
- Chen , B. and Saffman , P. G. 1979 . “Steady gravity-capillary waves on deep water-1. Weakly nonlinear waves” . Stud. Appl. Math. , 60 : 183 – 210 .
- Chossat , P. and Dias , F. 1995 . “The 1:2 resonance with O(2) symmetry and its applications in hydrodynamics” . J. Nonlinear Science , 5 : 105 – 129 .
- Christodoulides , P. and Dias , F. 1994 . “Resonant capillary-gravity interfacial waves” . J. Fluid Mech. , 265 : 303 – 343 .
- Christodoulides , P. and Dias , F. 1995 . “Stability of capillary-gravity waves between two bounded fluids” . Physics of Fluids , 12 : 3013 – 3027 .
- Dias , F. and Iooss , G. 1996 . “Capillary-gravity interfacial waves in infinite depth” . Eur. J Mech. B/Fluids , 15 : 367 – 393 .
- Drazin , P. G. 1970 . “Kelvin-Helmholtz instability of finite amplitude” . J. Fluid Mech. , 42 : 321 – 335 .
- Hasimoto , H. and Ono , H. 1972 . “Nonlinear modulation of gravity waves” . J. Phys. Soc. of Japan , 33 : 805 – 811 .
- Jones , M. C. W. 1997 . “Nonlinear ripples of Kelvin-Helmholtz type which arise from an interfacial mode interaction” . J. Fluid Mech. , 341 : 295 – 315 .
- Jones , M. C. W. 1999 . “A nonlinear multiple scales approach to modelling almost third harmonic interfaces” . Z. angew. Math. Phys. , 50 : 47 – 63 .
- McGoldrick , L. F. 1970 . “On Wilton's ripples: a special case of resonant interactions” . J. Fluid Mech. , 42 : 193 – 200 .
- Nayfeh , A. H. 1970 . “Finite amplitude surface waves in a liquid layer” . J. Fluid Mech. , 40 : 671 – 684 .
- Nayfeh , A. H. 1971 . “Second harmonic resonance in the interaction an airstream with capillary gravity waves” . J. Fluid Mech. , 48 : 384 – 395 .
- Nayfeh , A. H. and Hassan , S. D. 1971 . “The method of multiple scales and nonlinear dispersive waves” . J. Fluid Mech. , 48 : 463 – 475 .
- Nayfeh , A. H. and Saric , W. S. 1972 . “Nonlinear waves in a Kelvin-Helmholtz flow” . J. Fluid Mech. , 55 : 311 – 327 .
- Reeder , J. and Shinbrot , M. 1981 . “On Wilton ripples II: rigorous results” . Arch. Rat. Mech. Anal. , 77 : 115 – 135 .
- Strizhkin , I. I. and Raletnev , V. I. 1986 . “Experimental studies of three- and four-wave resonant interactions of surface sea waves” . Atmospheric and Ocean Physics , 22 : 311 – 314 .
- Wilton , J. R. 1915 . “On ripples” . Phil. Mag. , 29 : 688 – 700 .
- Zakharov , V. E. 1968 . “Stability of periodic waves of finite amplitude on the surface of a deep fluid” . J. Appl. Mech. Tech. Phys. , 2 : 190 – 194 .