A two-dimensional numerical model for solving the Navier–Stokes equations was developed to investigate the local scour around a submarine pipeline with a spoiler. Both the suspended load and the bed load were considered in the present numerical model. The focus of the present study is to investigate the effects of the spoiler length on the hydrodynamic forces on the pipeline and the spoiler as well as the local scour around the submarine pipeline. The corresponding numerical results show that the mean drag coefficients of the pipeline and the spoiler increase with the increase of the spoiler length. As for the mean lift coefficient, a general decreasing trend with the increasing spoiler length is observed for the pipeline. However, the mean lift coefficient of the spoiler first increases and then decreases with the increasing spoiler length. In addition, it is found that a larger spoiler length leads to a deeper scour depth, and an empirical equation was proposed for predicting the non-dimensional scour depth of submarine pipelines with non-dimensional spoiler length based on the numerical results.

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.

Accurately simulating wave breaking is crucial for modeling hydrodynamics over steep coral reef slopes, yet it remains a challenge for Boussinesq-type models like FUNWAVE-TVD. The model’s standard hybrid breaking mechanism, triggered by a fixed free surface elevation-to-depth ratio ($\eta /d>0.8$), often lacks physical sensitivity to local slope and wave conditions prevalent in reef environments and suffers from inaccuracies associated with using η as a direct proxy for wave height (H). This study introduces and validates a novel, enhanced hybrid breaking module within FUNWAVE-TVD, specifically designed to overcome these limitations on steep slopes. The core novelty lies in the synergistic implementation of two key components: (1) replacing the fixed threshold with a dynamic, physically-based criterion derived from the Modified Goda formula (MGO) by Rattanapitikon and Shibayama, which calculates the breaking wave height ($H_b$) based on local depth, slope, and deep-water wavelength; and (2) developing and applying a practical method, using the wave vertical asymmetry relationship proposed by Yu and Li, to dynamically convert the calculated $H_b$ into an equivalent breaking surface elevation threshold (${\eta }_b$). This derived dynamic threshold (${\eta }_b/d$) is then used to trigger the model’s existing switch from Boussinesq to Nonlinear Shallow Water Equations (NSWE), allowing for energy dissipation via shock-capturing while retaining the physical basis of the MGO criterion. The performance of this enhanced module was rigorously evaluated against five laboratory experiments of regular waves breaking on impermeable slopes ranging from mild (1:10) to extremely steep (1:1), contrasting results with the original FUNWAVE-TVD. The modified model demonstrates significantly improved accuracy (model skill increases ranging from 10.16% to 42.49%) compared to the original model for breaking location and wave height prediction on steeper slopes ($m\ge 1:6$). Conversely, tests on the 1:1 slope confirmed the inherent limitations of the MGO criterion itself under surging breaker conditions ($m\ge 1:2.3$), highlighting the applicability range. This work provides a validated methodology for incorporating slope-aware, dynamic breaking criteria effectively into hybrid Boussinesq models, offering a more robust tool for simulating wave processes on steep reef topographies.