On the crest instabilities of steep surface waves

Journal of Fluid Mechanics

Volumn 336, Issue , 1997, Pages 51-68

  Longuet Higgins, Michael ^a   Tanaka, Mitsuhiro ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b GIFU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; ROTATIONAL FLOW; WATER WAVES;

IRROTATIONAL SURFACE WAVES; SUPERHARMONIC INSTABILITIES;

SURFACE WAVES;

INSTABILITY; SHALLOW WATER EQUATIONS; WAVES;

CREST INSTABILITIES; SURFACE WAVES; WAVE MODELLING; WAVE STEEPNESS;

EID: 0031126396     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096004028     Document Type: Article

References (16)

1. CLEAVER, R. P. 1981 Instabilities of surface gravity waves. PhD thesis, University of Cambridge.
2. JILLIANS, W. J. 1989 The superharmonic instability of Stokes waves in deep water. J. Fluid Mech. 204, 563-579.
3. KHARIF, C. & RAMAMONJIARISOA, A. 1990 On the stability of gravity waves on deep water. J. Fluid Mech. 218, 163-170.
4. LONGUET-HIGGINS, M. S. & CLEAVER, R. P. 1994 Crest instabilities of gravity waves. Part 1. The almost-highest wave. J. Fluid Mech. 258, 115-129.
5. LONGUET-HIGGINS, M. S., CLEAVER, R. P. & FOX, M. J. H. 1994 Crest instabilities of gravity waves. Part 2. Matching and asymptotic analysis. J. Fluid Mech. 259, 333-344.
6. LONGUET-HIGGINS, M. S. & DOMMERMUTH, D. G. 1997 Crest instabilities of gravity waves. Part 3. Nonlinear development and breaking. J. Fluid Mech. 336, 33-50 (referred to herein as LHD).
7. LONGUET-HIGGINS, M. S. & FOX, M. J. H. 1977 Theory of the almost-highest wave: the inner solution. J. Fluid Mech. 80, 721-741.
8. 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.
9. LONGUET-HIGGINS, M. S. & FOX, M. J. H. 1996 Asymptotic theory for the almost-highest solitary wave. J. Fluid Mech. 317, 1-19.
10. MACKAY, R. S. & SAFFMAN, P. G. 1986 Stability of water waves. Proc. R. Soc. Lond. A 406, 115-125.
11. SAFFMAN, P. G. 1985 The superharmonic instability of finite-amplitude water waves. J. Fluid Mech. 159, 169-174.
12. TANAKA, M. 1983 The stability of steep gravity waves. J. Phys. Soc. Japan 52, 3047-3055.
13. TANAKA, M. 1986 The stability of solitary waves. Phys. Fluids 29, 650-655.
14. TANAKA, M. 1995 On the "crest instabilities" of steep gravity waves. Workshop on Mathematical Problems in the Theory of Nonlinear Water Waves, CIRM, Luminy, France, May 1995 (Abstract only).
15. TANAKA, M., DOLD, J. W., LEWY, M. & PEREGRINE, D. H. 1987 Instability and breaking of a solitary wave. J. Fluid Mech. 185, 235-248.
16. ZUFIRIA, J. A. & SAFFMAN, P. G. 1986 The superharmonic instability of finite-amplitude surface waves on water of finite depth. Stud. Appl. Maths 74, 259-266.