Thomas A.A. Adcock

The available power from tidal stream turbines in the Pentland Firth

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.

Did the Draupner wave occur in a crossing sea

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 waves 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.

The physics of anomalous (‘rogue’) ocean waves

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.

Tidal power generation - A review of hydrodynamic modelling

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.

Estimating ocean wave directional spreading from an Eulerian surface elevation time history

The directional spreading of sea states is an important design parameter in offshore engineering. Wave directionality affects the resulting wave kinematics, which affects the forces exerted on offshore structures. In this paper, we develop a method for estimating the amount of spreading, when the only information available is the time history of free surface elevation at a single point in space. We do this by predicting the second-order bound waves that occur at the difference in frequency of two freely propagating waves. The magnitude of these second-order bound waves is a function of the angle between the interacting waves. Thus, it is possible to infer some information about spreading from a single-point time history. We demonstrate that this approach works for wave groups in a fully nonlinear numerical wave tank. We create a synthetic random sea state and introduce noise into the analysis and thus show that our approach is robust and insensitive to noise, even with a signal-to-noise ratio of unity in the difference waves. This approach is also applied to random waves in a physical wave tank where spreading was directly measured and also to a storm recorded in the North Sea. In all cases, we find our estimate of spreading is in good agreement with other measurements.

An electrical analogy for the Pentland Firth tidal stream power resource

Several locations in the Pentland Firth, UK, have been earmarked for the deployment of separate farms of tidal turbines. However, recent numerical modelling suggests that these farms will be inter-dependent and that they must work together to optimize their collective performance. To explain this inter-dependence, in this paper we develop an electrical circuit analogy to describe flow through the Pentland Firth, in which parallel connections in the circuit represent different sub-channels formed by the islands of Swona, Stroma and the Pentland Skerries. The analogy is introduced in stages, beginning with turbines placed in a single channel, then turbines placed in a sub-channel connected in parallel to another sub-channel, and finally more complicated arrangements, in which turbines are installed both in parallel and in series within a multiply connected channel. The analogy leads to a general formula to predict the tidal power potential of turbines placed in a sub-channel connected in parallel to another sub-channel, and a predictive model for more complicated multiply connected channel arrangements. Power estimates made using the formula and predictive model (which may be applied using only measurements of the undisturbed natural tidal hydrodynamics) are shown to agree well with numerical model predictions for the Pentland Firth, providing useful insight into how to best develop the resource.

Nonlinear dynamics of wave-groups in random seas: unexpected walls of water in the open ocean

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.

The nonlinear evolution and approximate scaling of directionally spread wave groups on deep water

The evolution of steep waves in the open ocean is nonlinear. In narrow-banded but directionally spread seas, this nonlinearity does not produce significant extra elevation but does lead to a large change in the shape of the wave group, causing, relative to linear evolution, contraction in the mean wave direction and lateral expansion. We use the nonlinear Schrödinger equation (NLSE) to derive an approximate analytical relationship for these changes in group shape. This shows excellent agreement with the numerical results both for the NLSE and for the full water wave equations. We also consider the application of scaling laws from the NLSE in terms of wave steepness and bandwidth to solutions of the full water wave equations. We investigate these numerically. While some aspects of water wave evolution do not scale, the major changes that a wave group undergoes as it evolves scale very well.

Energy storage inherent in large tidal turbine farms.

While wind farms have no inherent storage to supply power in calm conditions, this paper demonstrates that large tidal turbine farms in channels have short-term energy storage. This storage lies in the inertia of the oscillating flow and can be used to exceed the previously published upper limit for power production by currents in a tidal channel, while simultaneously maintaining stronger currents. Inertial storage exploits the ability of large farms to manipulate the phase of the oscillating currents by varying the farms drag coefficient. This work shows that by optimizing how a large farms drag coefficient varies during the tidal cycle it is possible to have some flexibility about when power is produced. This flexibility can be used in many ways, e.g. producing more power, or to better meet short predictable peaks in demand. This flexibility also allows trading total power production off against meeting peak demand, or mitigating the flow speed reduction owing to power extraction. The effectiveness of inertial storage is governed by the frictional time scale relative to either the duration of a half tidal cycle or the duration of a peak in power demand, thus has greater benefits in larger channels.

Tidal stream power in the Pentland Firth – long-term variability, multiple constituents and capacity factor

The Pentland Firth, Scotland, is one of the World’s prime locations for the eventual installation of large farms of tidal stream turbines. This paper seeks to improve the upper bound estimate of available power output obtained by Adcock et al. (2013) who used a depth-integrated numerical model of the region containing the Pentland Firth with the outer boundary forced solely by M2 and S2 tidal constituents. Herein, the analysis is extended to include six additional tidal constituents and the model run for 11.5 years, more than half of the 18.6-year lunar nodal cycle, to allow variations over this to be analysed. The consequent increase in available power is estimated, and the variation in power output over an 11-year period is examined. Although further power could theoretically be extracted from the additional six tidal constituents, this would require the tidal turbine farm to have such a low capacity factor that it would probably be economically unfeasible.