General Third-Order Solutions for Irregular Waves in Deep Water
Publication: Journal of Engineering Mechanics
Volume 125, Issue 7
Abstract
The third-order analytical solutions for the strong interactions among three free-wave components are derived using two well-known perturbation methods, namely, the mode-coupling method and the Zakharov equation method. A term-by-term comparison of their solutions shows that the two methods render virtually identical results. The validity and convergence range of the solution are investigated for the interacting free-wave components of various frequencies but within the frequency range of storm seas. It is found that the solution may encounter two types of convergence difficulties, which occur, respectively, in the cases (1) when two of the interacting free-wave components are of quite different frequencies; and (2) when two of the interacting free-wave components are very close in frequency but the frequency of the third free-wave component is relatively larger or smaller.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Benney, D. J. (1962). “Nonlinear gravity wave interactions.” J. Fluid Mech., Cambridge, U.K., 14, 577–584.
2.
Brueckner, K. A., and West, B. J. (1988). “Vindication of mode-coupled description of multiple scale water wave fields.” J. Fluid Mech., Cambridge, U.K., 196, 585–592.
3.
Chen, L. ( 1996). “General solution for strong wave-wave interaction in deep water,” PhD dissertation, Oc. Engrg. Program, Texas A&M University, College Station, Tex.
4.
Chen, L., and Zhang, J. (1996). “On interaction between intermediate-depth long waves and deep-water short waves.” J. Oc. Engrg., 25, 395–423.
5.
Hasselmann, K. (1962). “On the nonlinear energy transfer in a gravity-wave spectrum. Part 1: General theory.” J. Fluid Mech., Cambridge, U.K., 12, 481–500.
6.
Hogan, S. J., Gruman, I., and Stiassnie, M. (1988). “On the changes in phase speed of one train of water waves in the presence of another.” J. Fluid Mech., Cambridge, U.K., 192, 97–114.
7.
Holliday, D. (1977). “On nonlinear interactions in a spectrum of inviscid gravity-capillary surface waves.” J. Fluid Mech., Cambridge, U.K., 84, 737–749.
8.
Longuet-Higgins, M. S., and Phillips, O. M. (1962). “Phase velocity effects in tertiary wave interactions.” J. Fluid Mech., Cambridge, U.K., 12, 333–336.
9.
Longuet-Higgins, M. S., and Stewart, R. W. (1960). “Changes in the form of short gravity waves on long waves and tidal currents.” J. Fluid Mech., Cambridge, U.K., 8, 565–583.
10.
Phillips, O. M. (1960). “On the dynamics of unsteady gravity waves of finite amplitude. Part 1: The elementary interactions.” J. Fluid Mech., Cambridge, U.K., 9, 193–217.
11.
Pierson, W. J. Jr. (1993). “Oscillatory third-order perturbation solutions for sums of interacting long-crested stokes waves on deep water.” J. Ship Res., 37(4), 354–383.
12.
Stiassnie, M., and Shemer, L. (1984). “On modifications of the Zakharov equation for surface gravity waves.” J. Fluid Mech., Cambridge, U.K., 143, 47–67.
13.
West, B. J., Watson, K. M., and Thomson, A. J. (1974). “Mode coupling description of ocean wave dynamics.” Phys. Fluids, 17, 1059–1067.
14.
Yuen, H. C., and Lake, B. M. (1982). “Nonlinear dynamics of deep-water gravity waves.” Advanced Appl. Mech., 22, 67–229.
15.
Zakharov, V. E. (1968). “Stability of periodic waves of finite amplitude on the surface of a deep fluid.” J. Appl. Mech. and Tech. Phys., 9, 190–194.
16.
Zhang, J., Chen, L., Ye, M., and Randall, R. E. (1996). “Hybrid wave model for unidirectional irregular waves. Part I: Theory and numerical scheme.” Appl. Oc. Res., 18, 93–110.
17.
Zhang, J., Hong, K., and Yue, D. K. P. (1993). “Effects of wavelength ratio on wave modeling.” J. Fluid Mech., Cambridge, U.K., 248, 107–127.
Information & Authors
Information
Published In
History
Received: Sep 24, 1998
Published online: Jul 1, 1999
Published in print: Jul 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.