Application of stokes, cnoidal, and fourier wave theories

Journal of Waterway, Port, Coastal and Ocean Engineering

Volumn 113, Issue 6, 1987, Pages 565-587

  Sobey, Rodney J ^a   Goodwin, Peter ^b   Thieke, Robert J ^a   Westberg, Robert J ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF BRADFORD   (United Kingdom)

^c Space and Naval Warfare Systems Center Pacific   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0023114838     PISSN: 0733950X     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-950X(1987)113:6(565)     Document Type: Article

References (26)

1. Abramowitz, M., and Stegun, I. A. eds., (1964). Handbook of mathematical functions. Dover, New York, N.Y.
2. Chaplin, J. R. (1980). “Developments of stream-function wave theory.” Coast. Engrg., 3, 179-205.
3. Chappelear, J. E. (1961). “Direct numerical calculation of wave properties.” J. Geophys. Res., 66, 501-508.
4. Cokelet, E. D. (1977). “Steep gravity waves in water of arbitrary uniform depth.” Proc. Roy. Soc, London, Series A, 286, London, England, 183-230.
5. Dalrymple, R. A. (1974). “A finite amplitude wave on a linear shear current.” J. Geophys. Res., 79, 4498-4504.
6. Dalrymple, R. A., and Solana, P. (1986). “Nonuniqueness in stream function wave theory.” J. Wtrway. Port, Coast. Oc. Engrg., ASCE, 112, 333-337.
7. Dean, R. G. (1965). “Stream function representation of nonlinear ocean waves.” J. Geophys. Res., 70, 4561-4572.
8. Dean, R. G. (1974). “Evaluation and development of water wave theories for engineering application.” Coast. Engrg. Res. Ctr., Special Rep. No. 1, 2 vols.
9. Dean, R. G., and Perlin, M. (1986). “Intercomparison of near-bottom kinematics by several wave theories and field and laboratory data.” Coast. Engrg., 9, 399-437.
10. Ebbesmeyer, C. E. (1974). “Fifth-order Stokes wave profiles.” J. Wtrways. Harbors and Coast. Engrg. Div., ASCE, 100, 264-265.
11. Fenton, J. D. (1979). “A high-order cnoidal wave theory.” J. Fluid Mech., 94, 129-161.
12. Fenton, J. D. (1985). “A fifth-order Stokes theory for steady waves.” J. Wtrway. Port, Coast, and Oc. Engrg., ASCE, 111, 216-234. (See also Errata, 1987, 113, 437-438.)
13. Fenton, J. D. (1987). “The numerical solution of steady water wave problems.” Computers and Geosci., 13, to appear.
14. Fenton, J. D., and Gardiner-Garden, R. S. (1982). “Rapidly-convergent methods for evaluating elliptic integrals and theta and elliptic functions.” J. Australian Math. Soc, Series B, 24, 47-58.
15. Huang, M-C, and Hudspeth, R. T. (1984). “Stream function solutions for steady water waves.” Continental Shelf Res., 3, 175-190.
16. Laitone, E. V. (1960). “The second approximation to cnoidal and solitary waves.” J. Fluid Mech., 9, 430-444.
17. Le Mehaute, B., Lu, C-C, and Ulmer, E. W. (1984). “Parameterized solution to nonlinear wave problem.” J. Wtrway. Port, Coast. Oc. Engrg., 110, 309-320.
18. Longuet-Higgins, M. S. (1975). “Integral properties of periodic gravity waves of finite amplitude.” Proc, Roy. Soc, London, Series A, 342, London, England, 157-174.
19. Nishimura, H., Isobe, M., and Horikawa, K. (1977). “Higher-order solutions of the Stokes and cnoidal waves.” J. Fac ofEngrg., Univ. of Tokyo, Series B, 34, Tokyo, Japan, 267-293.
20. Rienecker, M. M., and Fenton, J. D. (1981). “A Fourier approximation method for steady water waves.” J. Fluid Mech., 104, 119-137.
21. Schwartz, L. W. (1974). “Computer extension and analytical continuation of Stokes' expansion for gravity waves.” J. Fluid Mech, 65, 553-578.
22. Skjelbreia, L., and Hendrickson, J. (1962). “Fifth-order gravity wave theory.” Proc. 7th Int. Conf. Coast. Engrg., ASCE, The Hague, The Netherlands, 184-196.
23. Sobey, R. J. (1987). Discussion of “Nonuniqueness in stream function wave theory” by R. A. Dalrymple and P. Solana. J. Wtrway., Port, Coast., and Oc. Engrg., ASCE, 113, to be published.
24. Ursell, F. (1953). “The long-wave paradox in the theory of gravity waves.” Procs., Cambridge Phil. Soc, 49, 685-694.
25. Vanden-Broeck, J. M., and Schwartz, L. W. (1979). “Numerical computation of steep gravity waves in shallow water.” Phys. of Fluids, 22, 1868-1871.
26. Wiegel, R. L. (1960). “A presentation of cnoidal wave theory for practical application.” J. Fluid Mech., 7, 273-286.