Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas

Xiao Liang; Fang Xinhua

doi:10.1007/BF02849786

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Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas

OriginalPaper | Updated：2023-05-16

- Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas
- Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas
- 海洋湖沼学报（英文） 1991年9卷第1期页码：25-32
- Affiliations：
  
  1. South China Sea Institute of Oceanology
  2. Ocean University of Qingdao
- Author bio：
- Funds：
  
  Project supported by the National Natural Science Foundation of China.
- DOI：10.1007/BF02849786
  中图分类号：
- 纸质出版：1991
- Accepted：
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Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas[J]. 海洋湖沼学报（英文）, 1991,9(1):25-32.

Liang, X., Xinhua, F. Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas., Chin. J. Ocean. Limnol. 9, 25–32 (1991). https://doi.org/10.1007/BF02849786
Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas[J]. 海洋湖沼学报（英文）, 1991,9(1):25-32. DOI： 10.1007/BF02849786.

Liang, X., Xinhua, F. Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas., Chin. J. Ocean. Limnol. 9, 25–32 (1991). https://doi.org/10.1007/BF02849786 DOI：

摘要

Abstract

Some approximate formulas

based on the internal- wave directional spectral model established by Schott and Willebrand (1973)

of vertically standing wavemode eigenfunctions and a dispersion relation of internal waves in shallow seas are presented. An optimization method to estimate internal wave directional spectra is described and the confidence interval expression of the estimates is established. The GM spectral model of oceanic internal waves cannot be used in shallow seas (01 bers

1983). Internal waves in shallow seas have two origins: oceanic (those generated in and propagating from the deep sea and ocean) and local (Phillips

1977). As both reveal obvious propagation orientations

it is important to investigate the directional properties of the internal wave field. Though cross correlation function or cross-spectrum analyses can reveal the directional properties in some degree (Fang et al.

1984

and Fang

1987)

internal- wave directional spectrum analysis can further estimate the main propagation directions of wave components with different modenumbers and frequencies. So the latter is a more effective analysis tool. Because internal- wave directional spectrum analysis requires high quality data and long computer time

there are very few study reports so far on this subject. Among them. Schott and Willebrands' (1973) work is noteworthy. On the supposition

of linearization

they derived an internal- wave directional spectrum model. Internal-wave directional-spectra in shallow seas are investigated in the present study with their work as reference.

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references

Fang Xinhua, 1987. Analysis of spectral properties of internal waves on the continental shelf off Sydney, Australia.Acta Oceanologica Sinica 9(3): 294–301 (in Chinese).

Fang Xinhua, F. M. Boland and G. R. Cresswell, 1984. Further observations of high-frequency current variations on the continental shelf near Sydney, New South Wales,Aust. J. Mar. Freshw. Res. 35: 611–618.

Fang Xinhua and Xiao Liang, 1991. Directional spectrum analysis of internal waves in the sea off Sydney, Australia.Chin. J. Oceanol. Limnol. 9(1).

Olbers, D. J., 1983. Models of the oceanic internal wave field.Rev. Geophy., Space Phys. 21 (7): 1567–1606.

Phillips O. M., 1977. The Dynamics of the Upper Ocean, 2nd ed. Cambridge University Press, New York, 336 pp.

Schott F. and J. Willebrand 1973. On the determination of internal- wave directional spectra from moored instruments.J. Marine Res. 31 (2): 116–134.

Wang Deren, 1979. Methods to Solve Nonlinear Equation Sets and Optimization Methods. High Education Press, Beijing, 272 pp. (in Chinese).

Xi Shaolin and Zhao Fengzhi, 1983. Methods of Optimized Calculation. Shanghai Science and Technology Press, Shanghai, 461 pp. (in Chinese).

Zhou Gairong, 1984. Probability and Statistics. High Education Press, Beijing, 697 pp. (in Chinese).

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