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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 253401, 12 pages
On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System
1Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua city 500, Taiwan
2International Wave Dynamics Research Center, National Cheng Kung University, Tainan 701, Taiwan
3Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
4Tainan Hydraulic Laboratory, National Cheng Kung University, Tainan 701, Taiwan
Received 24 December 2012; Accepted 19 March 2013
Academic Editor: Kuppalapalle Vajravelu
Copyright © 2013 Chi-Min Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. G. Stokes, “On the theory of oscillatory waves,” Transactions of the Cambridge Philosophical Society, vol. 8, pp. 441–455, 1847.
- M. S. Longuet-Higgins and R. W. Stewart, “Radiation stress and mass transport in gravity waves, with application to "surf beats",” Journal of Fluid Mechanics, vol. 13, pp. 481–504, 1962.
- M. S. Longuet-Higgins and R. W. Stewart, “Radiation stresses in waterwaves: a physical discussion with applications,” Deep Sea Research, vol. 11, pp. 529–562, 1964.
- N. E. Ottesen-Hansen, “Long period waves in natural wave trains,” Progress Reports 46, Institute of Hydrodynamics and Hydraulic Engineering, Technical University Denmark, Lyngby, Denmark, 1978.
- R. G. Dean and N. J. Sharma, “Simulation of wave systems due to nonlinear directional spectra,” in Proceedings of International Symposium Hydrodynamics in Ocean Engineering, vol. 2, p. 1211, The Norwegian Institute of Technology, 1981.
- S. E. Sand and E. P. D. Mansard, “Reproduction of higher harmonics in irregular waves,” Ocean Engineering, vol. 13, no. 1, pp. 57–83, 1986.
- H. A. Schäffer, “Second-order wave maker theory for irregular waves,” Ocean Engineering, vol. 23, pp. 47–88, 1996.
- J. N. Hunt, “Interfacial waves of finite amplitude,” La Houille Blanche, vol. 16, pp. 515–531, 1961.
- S. A. Thorpe, “On the shape of progressive internal waves,” Philosophical Transactions of the Royal Society. London A, vol. 263, no. 1145, pp. 563–614, 1968.
- Y. Tsuji and Y. Nagata, “Stokes' expansion of internal deep water waves to the fifth order,” Journal of the Oceanographical Society of Japan, vol. 29, no. 2, pp. 61–69, 1973.
- J. Y. Holyer, “Large amplitude progressive interfacial waves,” Journal of Fluid Mechanics, vol. 93, no. 3, pp. 433–448, 1979.
- M. Umeyama, “Experimental and theoretical analyses of internal waves of finite amplitude,” Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 128, no. 3, pp. 133–141, 2002.
- J. B. Song, “Second-order random wave solutions for internal waves in a two-layer fluid,” Geophysical Research Letters, vol. 31, no. 15, pp. L15302–L15304, 2004.
- C. M. Liu, “Second-order random internal and surface waves in a two-fluid system,” Geophysical Research Letters, vol. 33, no. 6, p. L06610, 2006.
- T. Levi-Civita, “Détermination rigoureuse des ondes permanentes d'ampleur finie,” Mathematische Annalen, vol. 93, no. 1, pp. 264–314, 1925.
- S. E. Sand, “Wave grouping described by bounded long waves,” Ocean Engineering, vol. 9, no. 6, pp. 567–580, 1982.