基于广义高阶非线性薛定谔方程深海内波传播的数值模拟  

The Numerical Simulation of Deep-sea Internal Wave Propagation Based on Generalized Higher-order Nonlinear Schrdinger Equation

作　　者：石磊[1] 许晓革[2] 孟祥花[1] 

机构地区：[1]北京信息科技大学理学院,北京100192 [2]北京物资学院信息学院,北京101149

出　　处：《数学的实践与认识》2017年第9期190-197,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61471406;11401031)

摘　　要：基于与实际海洋背景参数相关的广义高阶非线性薛定谔方程,首先讨论了不同的海洋环境参数对方程的非线性项和频散项的影响;然后通过有限差分算子给出了方程的二阶三层数值差分格式,并且分析了该差分格式的稳定性与精度阶;最后又通过得到的差分格式数值模拟了不同的海洋环境参数下深海内波的传播情况,结果显示:内波由深海向浅海的传播过程中,随着总水深的变化,发生了分裂现象,并且密度差之比越大,波的分裂速度越快.The paper first discuss the influence of different marine environment parameters on the nonlinear term and the dispersion term based on the generalized higher-order nonlin- ear SchrSdinger （GHNLS） equation with real ocean background parameters. Then the two order three layer numerical difference scheme of the equation are given by the finite difference operators, and the stability and precision order of the difference scheme are analyzed. Finally we also numerical simulate the propagation situation of deep-sea internal wave with different marine environment parameters by the numerical difference scheme, the results shows： In the process of the propagation of the deep sea to the shallow sea, internal waves happens splitting phenomenon, with the change of the total water depth and the greater the density difference, the faster the splitting of the waves.

关 键 词：广义高阶非线性薛定谔方程 深海内波 数值差分格式 

分 类 号：P731.24[天文地球—海洋科学]