Kinematics Prediction by Stokes and Fourier Wave Theories
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 116, Issue 1
Abstract
Recent laboratory measurements of wave kinematics indicate that the horizontal velocity under the crest is smaller than that under the trough in the range of intermediate to deep water waves. The mathematically correct fifth‐order Stokes and Fourier wave theories can better predict the measured behavior if a zero uniform coflowing mass transport velocity is included in the solution algorithms. This is contrary to the conclusions made by Engevik and by Gudmestad and Connor. Horizontal velocity predictions from the Stokes and Fourier wave theories are in general more accurate than the deep‐water Green function method of Engevik and the second order stretching method of Gudmestad and Connor. The necessary correction procedure when using the Stokes and Fourier wave theories with a specified Eulerian current to predict the wave kinematics in a close flume with zero net flow over depth is also discussed in this paper.
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References
1.
Chakrabarti, S. K. (1971). Discussion of“Dynamics of single point mooring in deep water,” by J. H. Nath and M. P. Felix. J. Wtrwy., Harb. and Coast. Engrg. Div., ASCE, 97(3), 588–590.
2.
Chaplin, J. R. (1980). “Development of stream‐function wave theory.” Coast. Engrg., 3(3), 179–205.
3.
Dalrymple, R. A. (1974). “A finite amplitude wave on a linear shear current.” J. Geophys. Res., 79(30), 4498–4504.
4.
Dean, R. G. (1965). “Stream function representation of nonlinear ocean waves.” J. Geophys. Res., 70(18), 4561–4572.
5.
Dean, R. G. (1974). “Evaluation and development of water wave theories for engineering application.” Special Report No. 1, Coast. Engrg. Res. Center, Fort Belvoir, Va.
6.
Engevik, L. (1987). “A new approximate solution to the surface wave problem.” Appl. Oc. Res., 9(2), 104–113.
7.
Fenton, J. D. (1985). “A fifth‐order Stokes theory for steady waves.” J. Wtrway., Port, Coast, and Oc. Engrg., ASCE, 111(2), 216–234.
8.
Fenton, J. D. (1987). Errata to“A fifth‐order Stokes theory for steady waves.” J. Wtrway., Port, Coast, and Oc. Engrg., ASCE, 113(4), 437–438.
9.
Fenton, J. D. (1988). “The numerical solution of steady water wave problems.” Computers & Geosciences, 14(3), 357–368.
10.
Gudmestad, O. T., and Connor, J. J. (1986). “Engineering approximations to nonlinear deepwater waves.” Appl. Oc. Res., 8(2), 76–88.
11.
Huang, M.‐C., and Hudspeth, R. T. (1984). “Stream function solutions for steady water waves.” Continental Shelf Res., 3(2), 175–190.
12.
Huang, M.‐C. (1989). “Improved algorithm for stream function wave theory.” J. Wtrway., Port, Coast, and Oc. Engrg., ASCE, 115(1), 130–135.
13.
Rienecker, M. M., and Fenton, J. D. (1981). “A Fourier approximation method for steady water waves.” J. Fluid Mech., 104, 119–137.
14.
Sobey, et al. (1987). “Application of Stokes, Cnoidal, and Fourier wave theories.” J. Wtrway., Port, Coast, and Oc. Engrg., ASCE, 113(6), 565–587.
15.
Stokes, G. G. (1847). “On the theory of oscillatory waves.” Trans. Cambridge Philosophical Society, 8, 441–455.
16.
“Wave kinematics in irregular waves.” (1982). Report M1628/MaTs VM‐1‐4, Delft Hydraulic Laboratory, Delft, The Netherlands.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 116 • Issue 1 • January 1990
Pages: 137 - 148
Copyright
Copyright © 1990 ASCE.
History
Published online: Jan 1, 1990
Published in print: Jan 1990
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