Experiments are contaminated by second-order error waves at sub- and super-harmonic frequencies when first-order wave generation is used. Herein, we investigate by experiment the implications of second-order wave generation theory for dynamic wave force and run-up on a vertical wall in shallow to intermediate water depth (k₀d=0.5−1.1). Results of short-duration experiments using focused wave groups generated according to first- and second-order theory are compared. We isolate linear, sub-, and super-harmonic contributions using combinations of inverted wave group time series and filtering. We derive theoretical predictions for narrow-banded second-order wave groups interacting with a vertical wall and use this to calculate depth-integrated force and run-up on the wall, which show close agreement with measured data. Comparisons reveal that sub-harmonic error waves are increasingly important in shallow depth, increasing wave run-up by up to 67% and dynamic force by up to 75% at k₀d=0.6 when compared to the case of correct (second-order) generation in a relatively short flume.

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Using linear (first-order) wave generation theory in laboratory experiments, leads to significant contamination of the wave field by free non-linear (second-order) error waves, increasingly so at shallower depths. Second-order wave generation theory has previously been established, and so has correct generation of the bound set-down, made up from second-order bound waves in the sub-harmonic part of the spectrum, for bichromatic and irregular wave fields in shallow to intermediate depth. In the present work, different from previous studies, we validate second-order wave theory explicitly for isolated wave groups, which provide a demanding test on the correct generation of sub-harmonic bound waves and the stroke length of the wavemaker. We do so for shallow to intermediate water depth, where some previous attempts at full elimination of sub-harmonic error waves have been hampered by limited paddle stroke. We overcome these limitations by applying second-order wavemaker theory to a piston-type paddle with an extended paddle stroke that can thence generate the bound set-down correctly. We show that sub-harmonic error waves are eliminated by considering wave groups in relative depths k₀d = 0.6–1.1, with important applications in coastal engineering experiments, such as run-up and overtopping.

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A rectangular barge consisting of multiple oscillating water columns (OWCs) is considered in this paper, hereinafter referred to as a multi–OWC platform. Each OWC chamber is enclosed by two partially submerged vertical walls and the deck of the platform. An incident wave produces oscillation of the water column in each OWC chamber and hence air is pumped by the internal water surface to flow through a Wells turbine installed at the chamber top. The effect of the turbine is characterised as a linear power take–off (PTO) system. A semi–analytical model based on linear potential flow theory and the eigen–function expansion method is developed to solve the wave radiation and diffraction problems of the multi–OWC platform. The hydrodynamic coefficients evaluated with direct and indirect methods of the model are shown to be in excellent agreement, and the energy conservation relationship of the multi–OWC platform is satisfied. The validated model is then applied to predict wave motion, dynamic air pressure, wave power extraction, and wave reflection and transmission coefficients of the multi–OWC platform. The effects of the PTO strategies, the number of chambers, the overall platform dimensions and the relative dimensions of adjacent chambers on wave power extraction and wave attenuation are investigated. A smaller–draft front wall and a larger–draft back wall are found to be beneficial for broadening the range of high–efficiency performance of the platform. The same wave transmission coefficient can be obtained by two multi–OWC platforms with inverse geometric constructions.@en

The integration of oscillating water column (OWC) wave energy converters into a coastal structure (breakwater, jetty, pier, etc.) or, more generally, their installation along the coast is an effective way to increase the accessibility of wave power exploitation. In this paper, a theoretical model is developed based on the linear potential flow theory and eigenfunction matching method to evaluate the hydrodynamic performance of an array of OWCs installed along a vertical straight coast. The chamber of each OWC consists of a hollow vertical circular cylinder, which is half embedded in the wall. The OWC chambers in the theoretical model may have different sizes, i.e. different values of the radius, wall thickness and submergence. At the top of each chamber, a Wells turbine is installed to extract power. The effects of the Wells turbine together with the air compressibility are taken into account as a linear power take-off system. The hydrodynamic and wave power extraction performance of the multiple coast-integrated OWCs is compared with that of a single offshore/coast-integrated OWC and of multiple offshore OWCs. More specifically, we analyse the role of the incident wave direction, chamber size (i.e. radius, wall thickness and submergence), spacing between OWCs and number of OWCs by means of the present theoretical model. It is shown that wave power extraction from the coast-integrated OWCs for a certain range of wave conditions can be significantly enhanced due to both the constructive array effect and the constructive coast effect.@en