WAVE-CURRENT MODEL USING VARIATIONAL PRINCIPLE

Abstract

 Because of its simplicity, the water depth-integrated equation based on a hydrostatic assumption (longwave model) is often used to simulate river flows. On the other hand, the Boussinesq equations should be used to simulate progressive waves, such as solitary waves. In other words, the accurate representation of the non-hydrostatic components is an important aspect, and previous studies have proposed depth-integrated equations based on variational principles. Therefore, in this study, we performed simulations of progressive waves and steady & rapid flows using the longwave and Wave-Current models using the Variational principle (WCV model) and investigated their fidelity and reliability. Furthermore, we also compared the results with a three-dimensional numerical model to explore the effect of vertical vortices in the cross-sectional plane. As a result, it was found that the WCV model should be used to simulate the flow in rapid flow conditions. Additionally, in flow fields where influential vortices are formed near the water surface, it was found that a three-dimensional numerical model capable of reproducing the vertical vortices should be used instead of the water depth-integrated equation with no vorticities.