## 1 Introduction
An important property of these nets is their capacity to sustain heavy loads on every single twine. In [PERSON] et al. [8], [PERSON] et al. [9], the authors carried out a numerical study of the steady loads on plane nets modeled as an inter-connected system of lumped masses and springs for the local definition of the resistance force. Using the lumped-mass method, [PERSON] et al. [10] developed a 3D net model, which validated their previous 2D net model for the investigation of the effects of the structure size ratio and mesh type on the deformation of the gravity cage in the current. [PERSON] et al. [11] studied the drag coefficient of flat netting subjected to a cross-sectional flow and developed a semi-empirical model for the drag coefficient as a function of the flow regime. Another example is the investigation of the structural response of these fishing gears, as seen in [PERSON] et al. [12]. As the structural integrity plays an important role in many of these applications, numerical methods [13] have to deliver accurate predictions. These innovative approaches, such as demonstrated in the studies by [PERSON] et al. [14], enable scientists and engineers to enhance the complexity of their aquaculture net modeling. They investigated the hydrodynamic responses of a semi-submersible offshore fish farm, in order to optimize the design, to guarantee its structural integrity, and ensure the safety of workers during intense wave events. Since a fishing net can change orientation with regard to the incoming flow, it is important to understand the effect of its angle of attack. For example, [PERSON] et al. [15], [PERSON] et al. [16], [PERSON] et al. [17], and [PERSON] et al. [18], [PERSON] et al. [19], [PERSON] et al. [20], [PERSON] et al. [21], [PERSON] and [PERSON] [22], [PERSON] et al. [23] studied the effects of the flow speed and angle of attack on the drag and lift forces on nets through numerical simulation, empirical formulation, and/or physical model experiments. As a matter of fact, as the angle between the flow direction and the plane net is getting smaller,a shielding effect can drastically impact the drag coefficient. The leading twine acts as a shield and sheds vortices, subsequently changing the flow features around the following twine, and so on. All of these multiple phenomena are in nature problematic for the design of netted devices such as trawls. Designing the netting of a trawl (an instrument that is used for sampling the surface or the upper layer of the ocean) includes the consideration of its hydrodynamic properties to ensure its efficiency. For instance, [PERSON] et al. [24] studied the drag characteristics and fluttering motions of a midwater trawl codend since they affect the catch and vice versa. The study of [PERSON] et al. [25] suggested empirical formulas of the hydrodynamic model in terms of drag and lift coefficients for knot-less fine-mesh minnow netting for application to manta trawls. These trawls are effective tools for collecting plankton and other marine organisms while minimizing disturbances to the aquatic environment and providing accurate scientific data. They are employed in numerous prominent scientific investigations, including the comprehensive research conducted by [PERSON] et al. [26, 27] on the abundance of microplastics (>500 \(\upmu\)m) and mesoplastics (0.5-5 cm) in the surface waters of the eastern North Pacific Ocean and the pelagic distribution of plastic debris and marine organisms in the upper layer of the North Atlantic Ocean or the study of [PERSON] et al. [28] on the concentrations of floating neustonic life in the North Pacific Garbage Patch. For our case, the System 002 is depicted above water in Figure 1a and underwater in Figure 1b. At first glance, the cleanup system in operation resembles a fishing net during trawling, but a closer examination reveals the following differences:  
* The cleanup system catches plastic at the sea surface. Trawling is mostly performed close to the sea bed or at mid-water depth.