The permeable submerged breakwater has gained popularity in recent days due to its merits of reducing incident wave energy without negatively impacting the aesthetics of the ocean view and allowing for water exchange. However, the effect of porosity on wave nonlinearity and turbulence motion close to the water/structure interface is not well resolved in the literature. This paper presents an experimental and numerical study of regular wave propagation over a permeable submerged breakwater with a wide top width. The laboratory experiments were conducted in a wave flume and included 45 test cases. The numerical simulations were performed utilizing validated olaFoam. The results show that the nonlinearity of the waves on the permeable submerged breakwater is weak, which can effectively suppress and reduce the second harmonic waves. A large amount of turbulent kinetic energy exists at the interface between the permeable submerged breakwater and the water body, which helps to dissipate wave energy. For the wider permeable submerged breakwater in this paper, the wave dissipation capacity is greatest when the porosity is between 0.2 and 0.3, and as the length of the breakwater increases, the energy transmission coefficient decreases, and the energy dissipation coefficient increases. Better wave attenuation is achieved when the permeable submerged breakwater has a certain porosity and a large width.

To accurately capture wave dynamics in porous media, the higher-order Boussinesq-type equations for wave propagation in deep water are derived in this paper. Starting with the Laplace equations combined with the linear and nonlinear resistance force of the dynamic conditions on the free surface, the governing equations were formulated using various independent velocity variables, such as the depth-averaged velocity and the velocity at the still water level and at an arbitrary vertical position in the water column. The derived equations were then improved, and theoretical analyses were carried out to investigate the linear performances with respect to phase celerity and damping rate. It is shown that Boussinesq-type models with Padé [4, 4] dispersion can be applied in deep water. A numerical implementation for one-dimensional equations expressed with free surface elevation and depth-averaged velocity is presented. Solitary wave propagation in porous media was simulated, and the computed results were found to be generally in good agreement with the measurements.

In order to reveal the impact of hydrodynamic conditions on the transport and diffusion of pollutants in Liaodong Bay in China, this article uses MIKE21 to establish a numerical model to simulate the hydrodynamic mechanisms of tidal currents and residual currents in Liaodong Bay. The model has been calibrated using observation data from 10 stations, and the simulation results of the tidal currents, Euler residual currents, Lagrangian residual currents, and particle tracking in Liaodong Bay have been calculated. Subsequently, a comparative analysis is conducted based on the abovementioned data and measured data, exploring the impact of hydrodynamic conditions on the transport and diffusion of COD in Liaodong Bay. The research results in this article indicate that high concentration COD areas are mainly concentrated in the coastal areas around the estuary of the Liao River and the Daliao River, and river input is the main source of COD in Liaodong Bay. The Euler residual circulation can form COD enrichment in some areas, which is significantly higher than the background concentration, and the large-scale transportation of COD after entering Liaodong Bay is determined by the Lagrangian residual current. The particle tracking results in the estuarine area can effectively characterize the actual transportation of pollutants. The results of the Lagrangian residual flow and particle tracking in the bay indicate that river pollutants are mainly transported to the west bank after entering Liaodong Bay. The distribution of a COD concentration of 1.5 mg/L confirms this finding. The research findings presented in this paper offer valuable insights into the spatial distribution and transportation mechanisms of pollutants. These results hold significant implications for pollution prevention and mitigation strategies in comparable bay environments.