In the present work, theoretical and experimental studies on the interaction of water waves with a truncated circular cylinder were performed. The cylinder, which is partly made of porous materials, possesses a porous sidewall and an impermeable bottom. A nondimensional parameter $b$ is adopted in the theoretic formulation to describe the porosity, which is not directly related to the opening ratio $τ$ of the porous materials. To validate the theoretical work and computed results, a series of model tests are carried out in a wave basin. Effort is made to establish an empirical relation between $b$ and $τ$ based on the comparison of the calculation and experimental data. The phenomenon of the sloshing mode that occurred at a certain wave number is observed, which might have an application in breakwaters. The validation of the Haskind relations is examined for the porous body. It is found that the damping coefficient consists of two parts. In addition to the component of conventional wave-radiating damping, there exists a second component caused by the porous effects.

The industrial integration of offshore wind power and marine ranches has been actively explored and developed in many countries. This emerging industrial synergy can significantly improve the ecological friendliness of offshore wind power and contribute to the development of the marine economy in the region. This industrial synergy is an important development direction for future offshore engineering. Artificial reefs (ARs) are critical components of marine ranches and are widely placed around offshore wind foundations (OWFs). The ARs can block the water flow and form a complex wake region behind it, which changes the original turbulence structure and reduces scour around the OWF. Therefore, determining the arrangement of ARs for scour protection around an OWF is of great engineering significance. In this study, a three-dimensional numerical model is established using a prototype of the first offshore wind power-marine ranch demonstration project in China. The turbulent change and sediment movement between the OWF and ARs are solved using the Reynolds-averaged Navier-Stokes (RANS) and sediment transport equations. Moreover, the variations in the maximum scour depth and scour volume around the OWF at different arrangements of ARs are explored. The results demonstrate that the arrangement of ARs weakens the horseshoe vortices in front of the OWF and destroys the vortex shedding behind the OWF, thereby producing a beneficial scour protection effect. Various arrangements of ARs have different effects on scour results around the OWF. Increasing the height of the AR could significantly reduce the scour results around the OWF and play an effective role in scour protection, followed by the tandem arrangement of ARs, whereas the parallel arrangement of ARs will produce negative scour effects. This study will serve a vital guiding role in the arrangement of ARs and practical significance for scouring protection around the OWF.

Based on fractal theory, a regular fractal is used to construct symmetrical reef models (e.g., cube and triangle reef models) with different fractal levels (n = 1, 2, 3). Using the concept of fractal dimension, we can better understand the spatial effectiveness of artificial reefs. The void space complexity index is defined to quantify the complexity of the internal spatial distribution of artificial reefs models under different levels. The computational fluid dynamics (CFD) flow simulation approach was used to investigate the effects of void space complexity on the flow field performances of the symmetrical artificial reef models. The upwelling convection index ($H_{upwelling}/H_{AR}$, $V_{upwelling}/V_{AR}$), wake recirculating index ($L_{wake}/L_{AR}$, $V_{wake}/V_{AR}$) and non-dimensionalized velocity ratio range were used to evaluate the efficiency of the flow field effect inside or around artificial reefs. The surface area and spatial complexity index of artificial reefs increase with increasing fractal level. The numerical simulation data shows that the Menger-type artificial reef models with a higher spatial complexity index have better flow field performances in the upwelling and wake regions. Compared to the traditional artificial reef models, the upwelling convection index ($V_{upwelling}/V_{AR}$) and recirculating index ($V_{wake}/V_{AR}$) of n = 3 fractal cube artificial reef increase by 37.5% and 46.8%, respectively. The efficiency indices of the upwelling region and wake region around the fractal triangle artificial reef model are 2–3 times those of the fractal cube artificial reef model when the fractal level is 3.