We propose a hyperbolic system of first-order equations that approximates the 1D Nwogu model of the shallow water theory for non-hydrostatic unsteady flows. Solitary waves in the framework of these models are constructed and studied. The evolution of solitary waves on a mildly sloping beach is considered. We show that the solution of the hyperbolic system practically coincides with the corresponding solution of the Nwogu dispersive equations. Steep forced water waves generated by a harmonically oscillating rectangular tank are studied both experimentally and numerically. A comparison of the solutions of the modified Green–Naghdi and Nwogu equations with the obtained experimental data is made.

我们提出了一个一阶方程的双曲线系统，该系统近似于非静水非稳态流动的浅水理论的一维 Nwogu 模型。在这些模型的框架内构建和研究孤立波。考虑了在温和倾斜的海滩上孤立波浪的演变。我们证明了双曲系统的解实际上与 Nwogu 色散方程的相应解一致。对谐波振荡矩形水箱产生的陡峭强制水波进行了实验和数值研究。将修改后的 Green-Naghdi 和 Nwogu 方程的解与获得的实验数据进行了比较。