Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$ th-harmonic force scales with the $n$ th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

Fluid resonance may occur in a narrow gap between two side-by-side vessels under wave actions, which can cause significant wave height amplification inside the gap and further induce large wave loads and motion responses of the vessel. Based on an open-sourced computational fluid dynamics (CFD) package, OpenFOAM, the steady-state gap resonance phenomenon formed in between two side-by-side boxes and triggered by the incident regular waves is simulated, where the upriver box keeps fixed and the downriver one heaves freely under wave actions. This article comprehensively investigates the influence of the vertical degree of freedom of the downriver box on the wave loads exerting on both boxes and further reveals how the relative position of the heaving box with respect to the incident wave direction affects the characteristics of wave loads during the steady-state gap resonance. The results show that both the normalized largest wave loads and the dimensionless wavenumber where the normalized largest wave loads occur are significantly affected by both the incident wave heights and the relative position of the heaving box to the incident wave direction.

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

A general frequency domain dynamic model based on the DIFFRACT code has been developed to predict the motion and power generation of the three-float multi-mode wave energy converter M4, modelled as a two-body problem. The machine has previously been shown experimentally and numerically to have broad-band high capture widths for the range of wave periods typical of offshore sites. The float sizes increase from bow to stern; the bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the rotational relative motion is damped to absorb power. The floats are approximately half a wavelength apart so the float forces and motion in antiphase generate relative rotation. Here regular waves representative of swell are investigated and the model is shown to give accurate predictions of experimental results for motion and power for small wave heights and motion which are representative of operational conditions. A linear damper is used to model the power take-off. Without changing the float geometry or the hinge position, adjusting the linear damping factor for each frequency is shown to increase the power by up to three times the experimental value, with a maximum close to the theoretical value for a single float. Increasing the height of the hinge point above the mid float increases the power for the higher periods but can reduce power at lower periods. Since float motion can be quite large, this result can only be indicative of qualitative trends. The effect of small rows has been investigated, up to five machines, and it is shown in particular how the performance of wave energy devices in a row was affected by the multi-body interactions and wave directions. These results are important since the optimum damping factor is shown to be frequency dependent, and increase power generation by up to three times. Furthermore, hydrodynamic interference between M4 machines in a row may significantly increase the power generation when appropriate spacings are chosen.

With the increasing demand for wind energy, the vertical axis wind turbine (VAWT) is attracting more and more attention. In order to design the VAWT array for better performance, the VAWT wake model needs to reflect the wake characteristics well. Based on the asymmetric wake characteristic, a new VAWT wake model is proposed in this paper, which is a combination of two semi Gaussian functions with different deviations, and can be called the “double semi Gaussian functions wake model”. The model is simple and has only four parameters (mean, amplitude, left deviation and right deviation). Compared with the traditional Gaussian and Top-hat model, this model can better reflect the asymmetric characteristic of the VAWT wake. In particular, it can describe the behavior of wake merging in the case of counter-rotating twin turbines. Based on this wake model, the velocity field of VAWT array can be reproduced accurately. The goal function is mainly based on the performance of a basic array unit, and it can ensure the rapidity of the optimization process. The optimal arrangements under two different criteria are analyzed. Moreover, the truncation ratio is introduced to ensure that the downstream turbine works at the rated condition, and the optimal arrangements under different truncation ratios are analyzed. In this paper, the proposed wake model provides a good choice for the preliminary design of the VAWT array, and some relevant suggestions on the array arrangement have been put forward.

Steep wave breaking on a vertical cylinder (a typical foundation supporting offshore wind turbines) will induce slam loads. Many questions on the important violent wave loading and the associated secondary load cycle remain unanswered. We use laboratory experiments with unidirectional waves to investigate the fluid loading on vertical cylinders. We use a novel three-phase decomposition approach that allows us to separate different types of nonlinearity. Our findings reveal the existence of an additional quasi-impulsive loading component that is associated with the secondary load cycle and occurs in the backwards direction against that of the incoming waves. This quasi-impulsive force occurs at the end of the secondary load cycle and close to the passage of the downward zero-crossing point of the undisturbed wave. Wavelet analysis showed that the impulsive force exhibits superficially similar behaviour to a typical wave-slamming event but in the reverse direction. To monitor the scattered wave field and extract run-up on the cylinder, we installed a four-camera synchronised video system and found a strong temporal correlation between the arrival time of the Type-II scattered wave onto the cylinder and the occurrence of this quasi-impulsive force. The temporal characteristics of this quasi-impulsive force can be approximated by the Goda wave impact model, taking the collision of the Type-II scattered waves at the rear stagnation point as the impact source.