# Extreme Wave Loading on a Vertical Circular Cylinder
## 1 Introduction
The approach was also extended to more complicated configurations, including wave impact on perforated structures by [20], breaking wave impact on permeable barriers by [21], and axisymmetric wave impact on a vertical cylinder by [17]. Recently, [22] developed a simpler analytical model based on a Newtonian momentum argument for describing the horizontal impulse on a rectangular solid deck. The model assumes that the momentum carried by the incident large wave crest is transferred perfectly into the impact on the vertical edge of the solid deck. This has the potential to yield a practical approach for providing satisfactory engineering predictions due to its simplicity and thus motivates this work. The possible application of the methodology to a vertical cylinder of curved surface is explored experimentally here. A certain portion of the incoming flow momentum may be diverted rather than captured by the circular cylinder because it is more streamlined when compared to the square solid box. For simplicity and as a starting point to inform more sophisticated work in the future, the slamming contribution to the force-time series is isolated by forcing the crest of a wave to hit a truncated cylinder with its bottom being at or above the mean still water level. The height of the breaker (i.e., the height of the impacting fluid) is modeled/simulated by the vertical distance between the wave crest and the cylinder bottom, i.e., the inundation level in this work. It is worth noting that in the aforementioned pressure-impulse theory (see, e.g., [18]), this is usually left as a free parameter determined by calibrating against the experimental measurements or more advanced numerical results. It is also our aim to investigate the importance of higher-order wave components driving nonlinear loading on a structure. Hence, we use focused wave groups [23] as input waves to impinge the truncated cylinder, facilitating the extraction of wave components at various orders via the so-called phase-separation method [24]. In the phase-separation method, the Stokes expansion in regular waves is generalized to wave groups (i.e., the magnitude of each higher-order wave component is proportional to the linear component amplitude to the corresponding power) and is assumed to be valid for the physical process of interest. This hypothesis has been testified to be appropriate for deep- and intermediate-water waves (e.g., [14; 24; 25]). The application of the methodology, and hence the engineering model for nonlinear wave loading proposed by [14], to shallow-water waves of large steepness (the possible offshore wind farms scenarios) will be assessed in this paper. In addition, the use of a transient wave group has three other attractive advantages that are worth noting. Firstly, it retains the spectral nature of the real ocean waves, and secondly, the measurements are not contaminated by reflected waves from physical wave tank walls, making the interpretation of results easier [14; 25]. Thirdly, it is demonstrated to be a good representation of an individual extreme wave event in random seas, see, e.g., [26; 27; 28]. This work will also provide insights into the nonlinear characteristics of extreme wave loading on a vertical truncated cylinder, although limited to the scenarios in which the offshore platform or the floating wind turbine foundation (i.e., the cylinder bottom) is moved above the free surface by water waves. In contrast to bottom-mounted cylinders, this is less explored and shows rather different loading characteristics. In this context, the work of [29; 30; 31] is worth mentioning. [29] assessed the performance of a frequency domain potential flow solver and a full CFD solver when applied to nonlinear regular wave-truncated cylinder interactions. Comparisons to the experiments carried out at MOERI [32] were performed. [30] investigated linear wave diffractions from a truncated cylinder, with its upper part being surrounded by a porous material.