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

Updated：2023-05-16

- Internal wave eigenmodes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid—A preliminary theoretical and experimental study
- Journal of Oceanology and Limnology Vol. 10, Issue 1, Pages: 44-56(1992)
- Affiliations：
- Author bio：
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- DOI：10.1007/BF02844299
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- Published：1992
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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：

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.

关键词

Keywords

references

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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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