A close one-term approximation to the highest Stokes wave on deep water

Ocean Engineering

Volumn 33, Issue 14-15, 2006, Pages 2012-2024

  Rainey, R C T ^a   Longuet Higgins, Michael S ^b  

^a ATKINS   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Approximation; Highest wave; Stokes wave; Waves in deep water

Indexed keywords

APPROXIMATION THEORY; INTEGRATION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; WAVE EQUATIONS;

DEEP WATER; HIGHEST WAVE; NUMERICAL INTEGRATION;

WATER WAVES;

APPROXIMATION THEORY; INTEGRATION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; WATER WAVES; WAVE EQUATIONS;

DEEP WATER; GRAVITY WAVE; NUMERICAL METHOD; STOKES FORMULA;

EID: 33746913499     PISSN: 00298018     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.oceaneng.2005.09.014     Document Type: Article

References (10)

1. Grant M.A. The singularity at the crest of a finite amplitude progressive Stokes wave. Journal of Fluid Mechanics 59 (1973) 257-262
2. Longuet-Higgins M.S. On the form of the highest progressive and standing waves in deep water. Proceedings of the Royal Society of London A 331 (1973) 445-456
3. Longuet-Higgins M.S., and Dommermuth D.G. Crest instabilities of gravity waves. Part 3. Nonlinear development and breaking. Journal of Fluid Mechanics 336 (1997) 33-50
4. Longuet-Higgins M.S., and Fox M.J.H. Theory of the almost-highest wave: the inner solution. Journal of Fluid Mechanics 80 (1977) 721-741
5. Longuet-Higgins M.S., and Tanaka M. On the crest instabilities of steep surface waves. Journal of Fluid Mechanics 336 (1997) 51-68
6. Schwartz L.W. Computer extension and analytic continuation of Stokes's expansion for gravity waves. Journal of Fluid Mechanics 62 (1974) 553-578
7. Stokes G.G. On the theory of oscillatory waves. Appendix B: considerations relative to the greatest height of oscillatory irrotational waves which can be propagated without change of form. Mathematical Physics Papers 1 (1880) 225-228
8. Whittaker E.T., and Watson G.N. A Course of Modern Analysis. fourth ed. (1940), Cambridge University Press, Cambridge, UK 608pp
9. Williams J.M. Limiting gravity waves in water of finite depth. Philosophical Transactions of the Royal Society of London Series A 302 (1981) 139-188
10. Williams J.M. Tables of Progressive Gravity Waves (1985), Pitman Publishing Co., London, UK 640pp