Nonlinear modulation of the short internal waves in the weakly stratified ocean

Xu Zhaoting; S. P. Shen

doi:10.1007/BF02850652

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Nonlinear modulation of the short internal waves in the weakly stratified ocean

OriginalPaper | Updated：2023-05-16

- Nonlinear modulation of the short internal waves in the weakly stratified ocean
- Nonlinear modulation of the short internal waves in the weakly stratified ocean
- 海洋湖沼学报（英文） 1991年9卷第4期页码：364-374
- Affiliations：
  
  Ocean University of Qingdao
- Author bio：
- Funds：
  
  This project is supported by the National Natural Science Foundation of China.
- DOI：10.1007/BF02850652
  中图分类号：
- 纸质出版：1991
- Accepted：
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Nonlinear modulation of the short internal waves in the weakly stratified ocean[J]. 海洋湖沼学报（英文）, 1991,9(4):364-374.

Zhaoting, X., Shen, S.P. Nonlinear modulation of the short internal waves in the weakly stratified ocean., Chin. J. Ocean. Limnol. 9, 364–374 (1991). https://doi.org/10.1007/BF02850652
Nonlinear modulation of the short internal waves in the weakly stratified ocean[J]. 海洋湖沼学报（英文）, 1991,9(4):364-374. DOI： 10.1007/BF02850652.

Zhaoting, X., Shen, S.P. Nonlinear modulation of the short internal waves in the weakly stratified ocean., Chin. J. Ocean. Limnol. 9, 364–374 (1991). https://doi.org/10.1007/BF02850652 DOI：

摘要

Abstract

A nonlinear evolution equation of 2-D short internal waves under condition of weak stratification—cubic Schrödinger equation—is derived by using the reductive perturbation method. Because αβ<0 in the Schrödinger equation

in the linear system the sideband perturbation for the harmonic wave modulation is neutrally stable. At the same time

there is also a sort of wave packet.—KdV envelope soliton. In the nonlinear system the dark soliton is obtained under condition of weak stratification. It is shown that the vertical perturbation of the Brunt-Väìsälä frequency plays a role in forming the KdV envelope soliton and dark soliton.

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references

Davey, A. and K. Stewartson F. R. S., 1974. On three-dimensional packets of surface wave. Proc. R. Soc. Lond. A338 pp. 101–110.

Hui, W. H. and J. Hamilton, 1979. Exact solution of a three-dimensional nonlinear Schrödinger equation applied to gravity waves.J. F. M. 13: 117–133.

Koop, C. G. and L. G. Redekopp, 1981. The interaction of long and short internal gravity waves: Theory and experiment.J. F. M. 111: 367–409.

Leonov, A. I. and Y. Z. Miropolsky, 1975a. Short wave approximation in the theory of nonlinear steady internal gravity waves.Phys. Atm. and Ocea. 11(11): 1169–1178 (in Russian).

Leonov, A. I. and Y. Z. Miropolsky, 1975b. On theory of nonlinear internal gravity waves.Phys. Atm. and Ocea. 11(5): 491–502 (in Russian).

Miropolsky, Y. Z., 1981. Dynamics of Internal Gravity Waves in Ocean, Hydrometeo. Publishing House, Leningrad pp. 304 (in Russian).

Mei, C. C., 1983. The Applied Dynamics of Ocean Surface Waves, A Wiley-Interscience Publication, New York, pp. 740.

Miles, J. W., 1979. On internal solitary waves.Tellus 31: 456–462.

Taniuti, T. and K. Nishikwa, 1977. Nonlinear Waves. Atomic Energy Publishing House, Beijing pp. 276 (Chinese translation).

Xu Zhaoting, 1989. The internal solitary waves in the stratified ocean.J. Ocean Uni. of Qingdao 19(3): 1–9 (in Chinese with English abstract).

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