Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation

AbstractRecent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these earlier simulations. Although qualitative agreement is achieved, the present model is found to be unable to reproduce accurately the findings of the earlier study. Model parameter tests are then used to demonstrate that the present Boussinesq-type formulation is not well-suited to modelling the propagation of waves over sudden depth transitions. The present study nonetheless provides useful insight into the complexity encountered when modelling this type of problem and outlines a number of promising avenues for further research.</jats:p

Performance of non-uniform tidal turbine arrays in uniform flow

Theoretical models suggest that in order to maximise their collective power out put, tidal turbines should be arranged in a single cross-stream row and optimally spaced to exploit local blockage effects. However, because it is assumed that the turbines within these arrays are identical, such models do not consider the possibility of enhanced power production through the exploitation of spanwise variations in local blockage and resistance. In this paper, we use depth-averaged numerical simulations to investigate whether the performance of a tidal turbine array can be further enhanced by varying solely the local blockage, solely the local resistance, or both local blockage and resistance together, across the array width. Our results suggest that for an initially uniform flow field, the optimal tidal turbine array is also uniform, that is to say that it comprises turbines of equal size, spacing, and resistance. This finding is encouraging because it is more cost-effective and much simpler to design each turbine to be the same and to operate in the same way. Together with earlier findings, these results also suggest a more general, and perhaps unsurprising, conclusion that tidal turbine arrays perform best when designed to match site-specific natural flow conditions

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 interdependent 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. © 2013 The Author(s) Published by the Royal Society. All rights reserved

The available power from placing tidal stream turbines in the Pentland Firth

This paper assesses an upper bound for the tidal stream power resource of the Pentland Firth. A depthaveraged 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 1.9GW, averaged over the spring-neap cycle. However, generation of significantlymore 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 channelmodels 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. © 2013 The Author(s) Published by the Royal Society. All rights reserved

On the shape and likelihood of oceanic rogue waves

We consider the observation and analysis of oceanic rogue waves collected within spatio-Temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25H s) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms

On tidal stream turbines placed off headlands

Many candidate sites for tidal stream energy extraction can be classified as headland sites. Understanding the tidal resource of such sites is of fundamental importance to the industry. This paper examines an upper bound for the power that might be generated from an idealised headland. The dependence of this on length of turbine rows, number of turbine rows, and turbine blockage ratio are examined. Conclusions are drawn from this which are applicable to real headland sites

Energy Input Amplifies Nonlinear Dynamics of Deep Water Wave Groups

A possible physical mechanism for the formation of freak waves on the open ocean is the localized interactions between wind and waves.Such interactions are highly complex and are currently poorly understood at the scale of an individual wave.Rather than attempt to model the detailed transfer of energy from wind to waves, we simply consider the modifications to wave group dynamics of adding energy to the system. We carried out numerical experiments on isolated wave groups using an excited version of the nonlinear Schrödinger equation. Energy input enhances any soliton-like structures relative to regular waves for unidirectional propagation. For directionally spread wave groups, energy input enhances the nonlinear changes to the shapes of focused wave groups: Groups contract in the mean wave direction and expand in the lateral direction to a significantly greater degree than observed for nonexcited wave groups. © by The International Society of Offshore and Polar Engineers

Modification of tidal resonance in the Severn Estuary by a barrage and lagoon

The Bristol Channel/Severn Estuary has some of the largest tides in the world with a mean spring tidal range of 12.2 m. Numerous proposals have been made to exploit this for energy extraction. However, the large tidal range is partially driven by tidal resonance and such systems can be sensitive to small changes. Thus, it is important to understand the impact of a barrage on the resonance of the system which in turn leads to an understanding of the environmental impact of building a barrage. In this paper, we examine the resonant response of the Bristol Channel system, with and without a barrage structure deployed, using a depth-averaged numerical model. We find that the barrage can alter the response of the Bristol Channel to excitation with higher frequencies than 12 h. However, the barrage causes very little change to the resonant response for longer periods including for the semi-diurnal periods which dominate the tides in the region. We also briefly examine the Swansea Lagoon scheme and find that this is too small to have a significant impact on the resonant response of the channel

THE FOCUSING OF UNI-DIRECTIONAL GAUSSIAN WAVE-GROUPS IN FINITE DEPTH: AN APPROXIMATE NLSE BASED APPROACH

The non-linear changes to a NewWave type wave-group are helpful in developing our understanding of the non-linear interactions which can lead to the formation of freak waves. In addition, Gaussian wave-groups are used in model tests where it is useful to have a simple model for their non-linear dynamics. This paper derives a simple analytical model to describe the nonlinear changes to a wave-group as it focuses. This paper is an extension to finite depth of the theory developed for deep water in Adcock and Taylor (2009) (Proc. Roy. Soc. A 465(2110)). The model is derived using the conserved quantities of the cubic nonlinear Schrodinger equation (NLSE). In deep water there are substantial changes to the group shape and spectrum as the wave-group focuses, and the characteristics of these changes are governed by the Benjamin-Feir Index. However, in finite depth the characteristics of the non-linear interactions change, reducing the non-linear changes to the group shape. The analytical model is validated against simulations using the NLSE and against full potential flow solutions using a QALE-FEMnumerical scheme. We also compare its predictions against experiments in a physical wavetank. We find that the NLSE, and thus analytical theories derived from it, capture the dominant physics in the evolution of narrowbanded wave-groups. Copyright © 2010 by ASME