论文标题
三层分层流体中内部孤立波的双曲线模型
Hyperbolic model of internal solitary waves in a three-layer stratified fluid
论文作者
论文摘要
我们得出了一个新的双曲模型，该模型描述了具有非静压压力分布的分层浅水中内波的传播。双曲线模型的构建基于使用其他“瞬时”变量。这样一来，人们就可以将分散多层绿色-NAGHDI模型减少为进化方程的一阶系统。主要的关注是对在Boussinesq近似不均匀底部的三层流的研究，并在中间层中的静水压力进行了额外的假设。制定了三层流的方程的双波利度条件，并研究了行进波类中的溶液。基于提出的双曲线和分散模型，进行了内部孤立波的产生和传播的数值计算，并给出了它们与实验数据的比较。在提出的三层双曲模型的框架内，进行了对称和非对称孤子样波的传播和相互作用的数值研究。
We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional `instantaneous' variables. This allows one to reduce the dispersive multi-layer Green--Naghdi model to a first-order system of evolution equations. The main attention is paid to the study of three-layer flows over uneven bottom in the Boussinesq approximation with the additional assumption of hydrostatic pressure in the intermediate layer. The hyperbolicity conditions of the obtained equations of three-layer flows are formulated and solutions in the class of travelling waves are studied. Based on the proposed hyperbolic and dispersive models, numerical calculations of the generation and propagation of internal solitary waves are carried out and their comparison with experimental data is given. Within the framework of the proposed three-layer hyperbolic model, a numerical study of the propagation and interaction of symmetric and non-symmetric soliton-like waves is performed.
