根据流体力学基本方程组,利用摄动展开、多重尺度变换等方法,推得3层海洋分层模式下的非线性薛定谔(NLS)方程,发展了描述内波传播的新模型;利用该方程与SAR遥感探测机理相结合,得到反演内波振幅的关系,并选取中国南海东沙岛附近和英国马林陆架外缘海域,进行内波参数反演研究。结果表明,该模型反演的内波振幅与实测值更接近,验证了理论模型的适用性。

An internal wave is a common phenomenon that occurs in the pycnocline of the ocean. Its proprieties are closely related with ocean parameters, such as stratification. An internal wave is normally generated by tidal currents that encounter rough topography at deep ocean. Many internal waves in the South China Sea (SCS) have been detected from remote images; as a result, research on these waves has become popular in recent years. With the objective of exploring internal wave propagation and accurate inversed internal wave parameters, this study investigates a new model. The NonLinear Schrdinger (NLS) equation is established in a three-layer stratification configuration fluid as the theoretical model, and the SAR remote sensing detective model is presented based on the NLS equation. The inverse relation of the internal wave parameters is also proposed.
The three-layer NLS equation is based on the basic equations of fluid dynamics. Assuming that ocean water is stratified in a three-layer model, the Laplace and Bernoulli formulas of hydromechanics are first used. By introducing the multiple scale and perturbation expansion method, the governing equation can then be transformed into the NLS equation. The analytic solution is also obtained, and the analysis of the physical significance of several parameters in the equation is provided.
The internal wave amplitude is inversed in the Dong Sha Atoll of the SCS and the Malin shelf edge of the United Kingdom to verify the accuracy of the model. Inversion results are in accordance with the in situ measurement data. Moreover, the results of the three-layer NLS equation are more accurate than the two-layer models, such as the KdV and two-layer NLS equation. This finding proves that our NLS equation in a three-layer system is suitable for studying internal wave parameters.
The three-layer NLS equation is quite close to real ocean conditions. A clear view of internal waves can be obtained with this model. The inversion results show that the three-layer NLS equation is more suitable for studying internal waves in the SCS and Malin shelf areas than the two-layers models.