This paper assesses an upper bound for the tidal stream power resource of the Pentland Firth. A depth-averaged numerical model of the tidal dynamics in the region is set-up and validated against field measurements. Actuator disc theory is used to model the effect of turbines on the flow, and to estimate the power available for generation after accounting for losses owing to mixing downstream of the turbines. It is found that three rows of turbines extending across the entire width of the Pentland Firth and blocking a large fraction of the channel can theoretically generate 1.9 GW, averaged over the spring–neap cycle. However, generation of significantly more power than this is unlikely to be feasible as the available power per additional swept area of turbine is too small to be viable. Our results differ from those obtained using simplified tidal channel models of the type used commonly in the literature. We also use our numerical model to investigate the available power from rows of turbines placed across various subchannels within the Pentland Firth, together with practical considerations such as the variation in power over the spring–neap tidal cycle and the changes to natural tidal flows which result from power extraction.

There is much speculation that the largest and steepest waves may need to be modelled with different physics to the majority of the waves on the open ocean. This review examines the various physical mechanisms which may play an important role in the dynamics of extreme waves. We examine the evidence for these mechanisms in numerical and physical wavetanks, and look at the evidence that such mechanisms might also exist in the real ocean.

Offshore wind is a source of clean, renewable energy of great potential value to the power industry in the context of a low carbon society. Rapid development of offshore wind energy depends on a good understanding of technical issues related to offshore wind turbines, which is spurring ongoing research and development programmes. Foundations of offshore wind turbines present one of the main challenges in offshore wind turbine design. This paper reviews the present state of knowledge concerning geotechnical and structural issues affecting foundation types under consideration for the support structures of offshore wind turbines, and provides recommendations for future research and development.

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Extracting power from the tide is a potential avenue for renewable energy production but is also a significant engineering challenge. This challenge has many different aspects but the basic problem is the hydrodynamic problem of converting the movement of the ocean into mechanical power. This paper presents a review of some of the hydrodynamic modelling techniques which can be used to model tidal barrages and tidal turbines. The analysis of these is broken down into different length scales, ranging from a single device, to an array of devices, and up to regional scales. As well as discussing modelling techniques some of the hydrodynamic problems, such as resource assessment and efficiency of power generation, are discussed.

The 'New Year Wave' was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a 'freak' or 'rogue' wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave's directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90• or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80• to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.

Recent experimental and numerical studies of surface gravity waves propagating over a sloping bottom have shown an increase in the probability of extreme waves can be triggered by depth variations in sufficiently shallow waters. This phenomenon is studied here by means of a Boundary Element Method with fast multipole acceleration to solve the fully nonlinear water wave equations. We focus on the case of a random, unidirectional wave field with prescribed statistical properties propagating over a submerged slope, and consider different depth variations, including a step. Validation is provided by comparing with experiments by Trulsen, Zeng & Gramstad (Phys. Fluids, 24, 097101 (2012)). Strongly non-Gaussian statistics are observed in a region localized near the depth transition, beyond which the statistics settle rapidly to the steady statistical state of finitedepth random wave fields. Using a harmonic separation technique, we show that the second-order terms are responsible for the change in the statistical properties near the depth transition. We explore in detail the effects of peak frequency, significant wave height, the inclination of the slope, and the depth of the shallower water side on the kurtosis, skewness and the excess probability of the crest height, including their spatial distributions.

This paper investigates the size and structure of large waves on the open ocean. We investigate how nonlinear physics modifies waves relative to those predicted by a linear model. We run linear random simulations and extract extreme waves and the surrounding sea-state. For each extreme event, we propagate the waves back in time under linear evolution before propagating the wave-field forward using a nonlinear model. The differences between large linear and nonlinear wave-groups are then examined. The general trends are that under nonlinear evolution, relative to linear evolution, there is, on average, little or no extra amplitude in the nonlinear simulations; that there is an increase in the width of the crest of the wave-group and a contraction of large wave-groups in the mean wave direction; that large waves tend to move to the front of a wave-packet meaning that the locally largest wave is relatively bigger than the wave preceding it; and that nonlinearity can increase the duration of extreme wave events. In all these trends, there is considerable scatter, although the effects observed are clear. Our simulations show that nonlinearity does play an important part in the formation of extreme waves on deep water.