Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.     

Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings

This paper is concerned with the mixed initial–boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects. We successfully establish uniform exponential and polynomial decay rates for the solutions to this initial–boundary value problem under much weak conditions concerning memory effects. More specifically, we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory-effect region includes a part of the system boundary, while the condition is a necessity in the previous literature; moreover, for the polynomial decay rates we only assume minimal conditions on the memory kernel function g, without the usual assumption of $g^{\prime }$ controlled by g.     

Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Analytical and numerical studies for Seiches in a closed basin with bottom friction

A standing wave oscillation in a closed basin, known as a seiche, could cause destruction when its period matches the period of another wave generated by external forces such as wind, quakes, or abrupt changes in atmospheric pressure. It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy, resulting in damages around the area. One condition that might restrict the resonance from occurring is when the bottom friction is present. Therefore, a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena. The study will be conducted for several closed basin shapes. The model will be solved analytically and numerically in order to determine the natural resonant period of the basin, which is the period that can generate a resonance. The computational scheme proposed to solve the model is developed using the staggered grid finite volume method. The numerical scheme will be validated by comparing its results with the analytical solutions. As a result of the comparison, a rather excellent compatibility between the two results is achieved. Furthermore, the impacts that the friction coefficient has on the resonance phenomena are evaluated. It is observed that in the prevention of resonances, the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin. In addition, non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.     

Flume testing of passively adaptive composite tidal turbine blades under combined wave and current loading

The tidal energy industry is progressing rapidly, but there are still barriers to overcome to realise the commercial potential of this sector. Large magnitude and highly variable loads caused by waves acting on the turbine are of particular concern. Composite blades with in-built bend-twist elastic response may reduce these peak loads, by passively feathering with increasing thrust. This could decrease capital costs by lowering the design loads, and improve robustness through the mitigation of pitch mechanisms. In this study, the previous research is extended to examine the performance of bend-twist blades in combined wave–current flow, which will frequently be encountered in the field. A scaled 3 bladed turbine was tested in the flume at IFREMER with bend-twist composite blades and equivalent rigid blades, sequentially under current and co-directional wave–current cases. In agreement with previous research, when the turbine was operating in current alone at higher tip speed ratios the bend-twist blades reduced the mean thrust and power compared to the rigid blades. Under the specific wave–current condition tested the average loads were similar on both blade sets. Nevertheless, the bend-twist blades substantially reduced the magnitudes of the average thrust and torque fluctuations per wave cycle, by up to 10% and 14% respectively.     

An experimental investigation into non-linear wave loading on horizontal axis tidal turbines

Tidal turbines are subject to large hydrodynamic loads from combinations of currents and waves, which contribute significantly to fatigue, extreme loading and power flow requirements. Physical model testing enables these loads and power fluctuations to be assessed and understood in a controlled and repeatable environment. In this work, a 1:15 scale tidal turbine model is utilised to further the fundamental understanding of the influence of waves on tidal turbines. A wide range of regular waves are generated in both following-current and opposing-current conditions. Wave frequencies range from 0.31 Hz to 0.55 Hz & wave heights from 0.025 m to 0.37 m in a fixed 0.81 m/s current velocity. Waves are selected and programmed specifically to facilitate frequency domain analysis, and techniques are employed to isolate the effect of non-linear waves on turbine power and thrust.Results demonstrate that wave action induces large variations in turbine power and thrust compared to current only conditions. For the range of conditions tested, peak values of thrust and power exceed current-only values by between 7%–65% and 13%–160% respectively. These wave-induced fluctuations are shown to increase with wave amplitude and decrease with wave frequency. Following wave conditions exhibit greater variations than opposing for waves with the same wave height and frequency due to the lower associated wavenumbers.A model is developed and presented to aid the understanding of the high-order harmonic response of the turbine to waves, which is further demonstrated using steady state coefficients under assumptions of pseudo-stationarity. This approach is proven to be effective at estimating wave-induced power and thrust fluctuations for the combinations of waves, currents and turbine state tested. The outcome of which shows promise as a rapid design tool that can evaluate the effect of site-specific wave–current conditions on turbine performance.     

Mono-components from Blaschke products as solutions of a wave equation

In this note, we prove that the uni-modular mono-components from Blaschke products in the unit disc are eigenvectors of the Sturm-Liouville operators and investigate a kind of wave equations with some initial conditions, which give rise to mono-components.