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.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 20 Nov 2020|
|Event||9th International Conference on Lavrentyev Readings on Mathematics, Mechanics and Physics - Novosibirsk, Russian Federation|
Duration: 7 Sep 2020 → 11 Sep 2020