The dispersion relation for nonlinear waves in a developing process

Gu Daifang; Yuan Yeli

doi:10.1007/BF02850412

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The dispersion relation for nonlinear waves in a developing process

OriginalPaper | Updated：2023-05-16

- The dispersion relation for nonlinear waves in a developing process
- The dispersion relation for nonlinear waves in a developing process
- 海洋湖沼学报（英文） 1986年4卷第3期页码：256-277
- Affiliations：
  
  Institute of Oceanology
- Author bio：
- Funds：
  
  Acknowledgment: It is our pleasure to acknowledge with thanks the encouragement of Prof. Mao Hanli in this investigation. We would also like to thank Prof. Yu Zhouwen and Prof. Huang Peiji for their careful examination of this manuscript and many stimulating discussion.;Contribution No. 1332 from the Institute of Oceanology, Academia Sinica.
- DOI：10.1007/BF02850412
  中图分类号：
- 纸质出版：1986
- Accepted：
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The dispersion relation for nonlinear waves in a developing process[J]. 海洋湖沼学报（英文）, 1986,4(3):256-277.

Daifang, G., Yeli, Y. The dispersion relation for nonlinear waves in a developing process., Chin. J. Ocean. Limnol. 4, 256–277 (1986). https://doi.org/10.1007/BF02850412
The dispersion relation for nonlinear waves in a developing process[J]. 海洋湖沼学报（英文）, 1986,4(3):256-277. DOI： 10.1007/BF02850412.

Daifang, G., Yeli, Y. The dispersion relation for nonlinear waves in a developing process., Chin. J. Ocean. Limnol. 4, 256–277 (1986). https://doi.org/10.1007/BF02850412 DOI：

摘要

Abstract

We derived the dispersion relation (correct to the second order in wave slope) of nonlinear waves in a developing process

proved that there are mainly three time scales in a developing process of nonlinear waves governed by coupling mechanisms. The three time scales are oscillation

evolution and developing time scales. We also proved that even in the developing process of nonlinear waves

there is no term in dispersion relation in proportion to the first order of wave slope. In a stationary case our results agreed with the discrete form obtained by Weber in 1977. Our computed results of wave speed in the wallops spectrum were in good agreement with the laboratory measurements made by Ramamonjiarisoa (1976) in energy-containing range.

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references

Barrick, D.E. and B.L. Weber, 1977. On the nonlinear theory for gravity waves on the ocean surface, Part 2, Interpretation and Application.J. Phys. Oceanog. 7: 11–22.

Chen Shuxing, 1981. Introduction to Partial Differential Equation. People Education Press, Beijing. PP. 1–360

Huang, N.E. and C.C. Tung, 1976. The dispersion relation for a nonlinear random gravity wave field.J. Fluid Mech. 75: 337–345.

Huang, N.E. and C.C. Tung, 1977. The influence of the directional energy distribution on the nonlinear dispersion relation in a random gravity wave field.J. Phys. Oceanog. 7: 403–414

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Yuan Y.L., N.E. Huang and C.C. Tung, 1983. On the nonlinear waves in a developing process, Part 1. The deivation of the governing equations.Chin. J. Oceanol. Limnol. 1(3): 258–271 (in Chinese with English abstract).

Yuan, Y.L., N.E. Huang and C.C. Tung, 1984. On the nonlinear waves in a developing process, Part 2. Instability analysis.Chin. J. Oceanol. Limnol. 2(1): 1–11 (in Chinese with English abstract).

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