# Regular Wave Effects on the Hydrodynamic Performance of Fine-Mesh Nettings in Sampling Nets
## 1 Introduction  
Fine-mesh netting, featuring mesh sizes from several millimeters down to micrometers, is commonly employed in the trawling of small fish species such as minnows, as well as in ichthyoplankton sampling efforts [1, 2, 3, 4, 5, 6]. Unlike standard mesh netting [7, 8, 9, 10], fine-mesh netting typically exhibits a higher solidity ratio--defined as the proportion of the projected area of the netting relative to its total enclosed area. Its hydrodynamic performance and filtration efficiency differ significantly from those of standard mesh netting [11, 12, 13, 14, 15, 16]. Additionally, the stability and fuel consumption of sampling nets made from high-solidity-ratio netting are strongly influenced by the hydrodynamic characteristics of the material. Notably, fluctuations in the towing speed during sea trials have been observed to affect the depth stability of midwater sampling nets, leading to deviations from the desired operational depth [17]. In addition, prior studies have demonstrated that in square-mesh configurations, the filtration efficiency improves with the increasing towing velocity and decreasing solidity ratio [18]. These findings underscore the importance of a thorough understanding of the hydrodynamic performance of fine-mesh netting in optimizing the design and functional reliability of modern sampling nets. Extensive research on the hydrodynamic performance of standard mesh-sized netting has primarily concentrated on structural parameters such as the solidity ratio, twine material, and the distinctions between knotted and knotless configurations [9; 10; 19; 20; 21]. In contrast, fine-mesh netting, due to its higher solidity ratio, generates significantly greater hydrodynamic resistance and gives rise to more intricate and turbulent flow structures in the surrounding fluid. Consequently, the hydrodynamic coefficient of fine-mesh netting is higher, and the velocity attenuation downstream of the netting is more pronounced compared to that of standard mesh netting in currents [11; 14; 15; 16]. However, when fishing gear operates at the ocean surface, it is concurrently subjected to wave forces, which significantly affect its stability. Several studies have thus examined the influence of different wave types (e.g., regular, irregular, and extreme waves) and wave conditions (e.g., wave period, wave height, and wave steepness) on the hydrodynamic performance of netting [22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. For example, [PERSON] et al. found that changes in the wave geometry did not necessarily show more pronounced effects on nets with higher solidity ratios compared to those with lower solidity ratios [23]. Furthermore, the horizontal force exerted by waves was approximately 10 times greater than the vertical force, and both forces increased with the solidity ratio of the netting [24]. The drag coefficient was observed to decrease with increasing Reynolds and Keulegan-Carpenter numbers [26; 32]. In addition, the hydrodynamic performance of biofouled netting (with marine organisms such as hydroids attached, thereby increasing the solidity ratio) has been investigated under wave conditions. The results indicated that biofouling significantly increased the drag force, with a more pronounced effect on drag than on inertial force, causing the wave force on biofouled netting to be as much as 3.88 times greater than that on clean netting [28; 33]. Despite its widespread application, the hydrodynamic behavior of fine-mesh netting--particularly clean netting with a high solidity ratio--under wave conditions has received limited scholarly attention. A comprehensive understanding of its hydrodynamic performance in wave environments is, therefore, essential, as it can inform the optimized design and structural refinement of sampling gear used in marine research and fisheries' operations. Numerous studies have investigated the hydrodynamic performance of netting through both physical experiments and numerical simulations.