Crest instabilities of gravity waves: Part 1. The Almost-Highest Wave

Journal of Fluid Mechanics

Volumn 258, Issue , 1994, Pages 115-129

  Longuet Higgins, Michael S ^a   Cleaver, R P ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Gas Research Centre   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CREST INSTABILITIES; CREST INSTABILITY; GRAVITY WAVE; GRAVITY WAVES; WAVE BREAKING;

CREST INSTABILITIES; GRAVITY WAVES; WAVE BREAKING;

CAPILLARY FLOW; DEFORMATION; GRAVITATION; STABILITY; WATER;

ALMOST HIGHEST WAVE VELOCITY; CREST INSTABILITY; RADIUS OF CURVATURE; SPILLING BREAKER;

GRAVITY WAVES;

EID: 0028160277     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112094003265     Document Type: Article

References (18)

1. BANNER, M. L. & PEREGRINE, D. H. 1993 Wave breaking in deep water.Ann. Rev. Fluid Mech. 25, 373–397.
2. BONMARIN, P. 1989 Geometric properties of deep-water breaking waves. J. Fluid Mech. 209, 405–433.
3. CLEAVER, R. P. 1981 Instabilities of surface gravity waves. PhD thesis, University of Cambridge, UK, 224 pp.
4. HOLTHUIJSEN, L. H. & HERBERS, T. H. C. 1986 Statistics of breaking waves observed as white-caps in the open sea.J. Phys. Oceanogr. 16, 290–297.
5. KJELDSEN, S. P. & MYRHAUG, D. 1980 Wave-wave interactions current-wave interactions and resulting extreme waves and breaking waves.Proc. 17th Intl Conf. Coastal Engng, pp. 2277–2303. ASCE.
6. LONGUET-HIGGINS, M. S. 1978a Some new relations between Stokes’s coefficients in the theory of gravity waves.J. Inst. Maths Applies. 22, 261–273.
7. LONGUET-HIGGINS, M. S. 1978b The instabilities of gravity waves of finite amplitude in deep water. I. Superharmonics.Proc. R. Soc. Lond. A 360, 471-488.
8. LONGUET-HIGGINS, M. S. 1981 On the overturning of gravity waves.Proc. R. Soc. Lond. A 376, 377–400.
9. LONGUET-HIGGINS, M. S. 1986 Bifurcation and instability in gravity waves.Proc. R. Soc. Lond. A 403, 167–187.
10. LONGUET-HIGGINS, M. S. 1988 Mechanisms of wave breaking in deep water. In Sea Surface Sound (ed. B. R. Kerman), pp. 1–30. Kluwer. 639 pp.
11. LONGUET-HIGGINS, M. S., CLEAVER, R. P. & FOX, M. J. H. 1994 Crest instabilities of gravity waves. Part 2. Matching and asymptotic expansion. J. Fluid Mech. 259, 333–344.
12. LONGUET-HIGGINS, M. S. & COKELET, E. D. 1976 The deformation of steep gravity waves. I. A numerical method of computation.Proc. R. Soc. Lond. A 350, 1–26.
13. LONGUET-HIGGINS, M. S. & COKELET, E. D. 1978 The deformation of steep gravity waves on water. II. Growth of normal-mode instabilities.Proc. R. Soc. Lond. A 364, 1–28.
14. LONGUET-HIGGINS, M. S. & FOX, M. J. H. 1977 Theory of the almost-highest wave: the inner solution. J. Fluid Mech. 80, 721–741 (referred to herein as LHF1).
15. LONGUET-HIGGINS. M. S. & FOX, M. J. H. 1978 Theory of the almost-highest wave. Part 2. Matching and analytic extension. J. Fluid Mech. 85, 769–786.
16. MICHELL, J. H. 1893 The highest waves in water.Phil. Mag. 36, 430–437.
17. TANAKA M. 1983 The stability of steep gravity waves.J. Phys. Soc. Japan 52, 3047–3055.
18. TULIN, M. P. & LI, J. J. 1991 A mechanism for wave deformation and breaking intermediated by resonant side-bands.Proc. IVTAM Symp. on Breaking Waves, Sydney, Australia July 1991 (ed. M. L. Banner & R. H. J. Grimshaw), pp. 21–37. Springer.