Tidal Current Modeling Using Shallow Water Equations Based on the Finite Element Method: Case Studies in the Qiongzhou Strait and Around Naozhou Island

Tidal currents are a crucial oceanic process with significant implications for marine engineering and the sustainable use of coastal and marine resources. This paper presents the development of a finite element numerical model to simulate tidal currents. The model was mathematically formulated using the shallow water equations, which are applicable to fluid dynamics where the horizontal scale is significantly larger than the vertical scale. The finite element method was employed to discretize and solve the equations, with the bottom slope source term incorporated into the pressure equation to ensure numerical consistency. Furthermore, characteristic line theory was applied to derive the relationship between boundary tidal levels and current velocities to satisfy boundary compatibility conditions. The model was initially applied to the Qiongzhou Strait, and the results demonstrated good agreement with observed data. Subsequently, the model was implemented at Naozhou Island and its adjacent waters. The results revealed that the tidal currents around Naozhou Island exhibit oscillatory flow patterns, with the flow direction near Donghai Island oriented northeast–southwest (NE-SW) and the flow direction near Leizhou Bay oriented northwest–southeast (NW-SE). This study provides a hydrodynamic basis for marine engineering projects and the sustainable utilization of marine resources in the Naozhou Island area.