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The Consistence Between the Stokes Wave Theory and General Wave Theory

Published online by Cambridge University Press:  05 May 2011

C.-M. Liu ,
H.-H. Hwung  and
R.-Y. Yang
C.-M. Liu*
Affiliation:
General Education Center, Chienkuo Technology University, Changhua City, Taiwan 50094, R.O.C.
H.-H. Hwung*
Affiliation:
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C
R.-Y. Yang*
Affiliation:
Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Associate Professor
**Professor
***Associate Researcher
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Abstract

The consistence between the Stokes wave theory and general wave theory is examined in this study. As well known, the nonlinear terms of Stokes wave are generated by the self-interaction of first-order wave. On the other side, using the general wave theory one can also obtain the nonlinear solutions according to the interaction of n waves with the same amplitude, frequency and phase. It is found that the inconsistence between these two wave trains arises due to the subharmonic effects included in general wave theory but not considered in the Stokes theory. In conclusion, these two theories are substantially different unless the Bernoulli constants are properly chosen for mathematical equivalence.

Keywords

Stokes theoryGeneral wave theoryConsistence
Type
Technical Note
Information
Journal of Mechanics , Volume 25 , Issue 3 , September 2009 , pp. N17 - N20
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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References

1.Nagata, Y., the Chinese Edition translated by Tang, L. W., Scientific and Technical Pub. Co. Ltd. (2004).Google Scholar
2.Liu, C. M., Hwung, H. H. and Kong, C. H., “The Unsteady Viscous Flow Generated by a Moving Porous Plate,” Journal of Mechanics, 24, pp. 145–152 (2008).CrossRefGoogle Scholar
3.Liu, C. M. and Liu, I. C., “A Note on the Transient Solution of Stokes' Second Problem with Arbitrary Initial Phase,” Journal of Mechanics, 22, pp. 349–354 (2006).Google Scholar
4.Stokes, G. G., “On the Theory of Oscillatory Waves,” Trans. Camb. Phil. Soc., 8, pp. 441–455 (1847).Google Scholar
5.Craik, A. D. D., “George Gabriel Stokes on Water Wave Theory,” Annu. Rev. Fluid Mech., 37, pp. 23–42 (2005).CrossRefGoogle Scholar
6.Longuet-Higgins, M. S. and Stewart, R. W., “Radiation Stress and Mass Transport in Gravity Waves with Application to “Surf Beats”,” J. Fluid Mech., 13, pp. 481–504 (1962).Google Scholar
7.Ottesen-Hansen, N. E., “Long Period Waves in Natural Wave Trains,” Prog. Rep., 46,Google Scholar
7a Inst. of Hydrodyn. and Hydraulic Engng., Tech. Univ. of Denmark, pp. 13–24 (1978).Google Scholar
8.Dean, R. G. and Sharma, N. J., “Simulation of Wave Systems Due to Nonlinear Directional Spectra,” Proc. Int. Symp. Hydrodyn. in Ocean Engng., The Norwegian Inst. of Technol. 2, pp. 1211–1222 (1981).Google Scholar
9.Dingemans, M. K., Water Wave Propagation Over Uneven Bottoms, Part 1, World Scientific Publishing Co., Singapore (1997).Google Scholar