Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study

Wang Yiming; Xu Zhaoting

doi:10.1007/BF02844299

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Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study

OriginalPaper | Updated：2023-05-16

- Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study
- Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study
- 海洋湖沼学报（英文） 1992年10卷第1期页码：44-56
- Affiliations：
- Author bio：
- Funds：
  
  This work is supported by the National Natural Science Foundation of China.
- DOI：10.1007/BF02844299
  中图分类号：
- 纸质出版：1992
- Accepted：
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Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study[J]. 海洋湖沼学报（英文）, 1992,10(1):44-56.

Yiming, W., Zhaoting, X. Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study., Chin. J. Ocean. Limnol. 10, 44–56 (1992). https://doi.org/10.1007/BF02844299
Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study[J]. 海洋湖沼学报（英文）, 1992,10(1):44-56. DOI： 10.1007/BF02844299.

Yiming, W., Zhaoting, X. Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study., Chin. J. Ocean. Limnol. 10, 44–56 (1992). https://doi.org/10.1007/BF02844299 DOI：

摘要

Abstract

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid. An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile $$\rho = \rho _m - \Delta \rho \pi ^{ - 1} tg^{ - 1} \left( {b^{ - 1} y} \right)$$ similar to that in our experiment were obtained theoretically. The resonant-interaction mechanism to 2nd order approximation is also discussed. The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition

i.e.

$$\omega _1 - \omega _3 - \omega _4 = 0$$

k 1+k 3+k 4=0

is examined. It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency.

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references

Davis, R. E. and A. Acrivos, 1967. The stability of oscillating internal waves.J. Fluid Mech. 53: 17–44.

Hasselmann, K., 1967. A criterion for nonlinear wave instability.J. Fluid Mech. 30: 737–739.

Martin, S. W. Simmons and C. Wunch, 1972. The excitation of resonant triads by single internal waves.J. Fluid Mech. 53: 17–44.

Nayfeh, A. H., 1973. Perturbation Methods, U. S. A. 423 pp. (Chinese translation).

Phillips, O. M., 1977. The Dynamics of Upper Ocean, Syndics of the Cambridge University Press, Cambridge 335 pp.

Roberts, J., 1973. Internal Gravity Wave in the Ocean, Marcel Dekker, Inc., New York 274 pp.

Schooley, A. H. and R. W. Stewart, 1963. Experiment with a self-propelled body submerged in a fluid with a vertical density gradient.J. Fluid Mech. 15: 83–96.

Thorpe, S. A., 1968. On the shape of progressive internal waves.Phil. Trans. 263: 589–596.

Xu Zhaoting and Wang Jingming, 1989. A small internal wave tank and its water supply, wave making and measuring systems.J. of Ocean University of Qingdao 18(1): 95–101 (in Chinese with English abstract).

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