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 an 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.

中文翻译：

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三层分层流体中内部孤立波的双曲模型

我们推导了一个新的双曲线模型，该模型描述了内部波在具有非静水压力分布的分层浅水中的传播。双曲模型的构建基于其他瞬时变量的使用。这使人们可以将色散多层Green-Naghdi模型简化为演化方程的一阶系统。主要关注在Boussinesq近似中不均匀底部上的三层流动的研究，并附加假设了中间层的静水压力。阐述了所获得的三层流方程的双曲条件，并研究了行波类的解。基于建议的双曲和色散模型，对内部孤立波的产生和传播进行了数值计算，并与实验数据进行了比较。在提出的三层双曲模型的框架内，对对称和非对称类孤子波的传播和相互作用进行了数值研究。