A simplified method to estimate tidal current effects on the ocean wave power resource
Introduction
The exploitation of ocean wave power as a renewable energy resource has generated much interest in academia and industry, and has inspired many inventors, with more than one thousand patents registered to date for wave energy technologies [1]. The accurate assessment of site-specific ocean wave resource is the first step in developing projects for wave energy extraction [2].
Wave-current interactions are routinely ignored in such resource assessments (e.g. Refs. [3], [4]), despite earlier research that illustrates the significant influence of tidal currents on wave properties, such as height and wavelength [5], [6], [7]. This is partly due to the high computational cost associated with running coupled wave-tide models; also, validating wave-current interaction effects in numerical models is a challenging task due the paucity of observations and the complexity of the physical processes involved.
The effect of tidal currents on the wave power resource has been considered in a few studies to date, on the basis of coupled wave-tide models. Barbariol et al. [8] demonstrated that the inclusion of wave-current interaction (WCI) effects could yield up to a 30% difference in wave power estimates at a location in the Gulf of Venice. The ROMS (Regional Ocean Modelling System) ocean model and SWAN (Simulating WAve Nearshore) wave model were used in coupled mode to conduct this study. Using the same modelling approach, Hashemi and Neill [9] showed that tidal currents can alter wave power by more than 10% in some regions of the northwest European shelf seas. They also briefly discussed a simple method to calculate this effect. However, in their method, they only considered the effect of tides on the wave group velocity, but the effect on wave height, which might be greater, was ignored. Furthermore, due to this limitation, no comparison with observations was made – which could have assessed the accuracy of the method. Saruwatari et al. [10] used a coupled model (SWAN and MOHID Water Modelling System [11]) to study the effect of WCI on the wave power, around Orkney. They reported an up to 200% increase in wave height, when waves and currents are opposing. However, they did not demonstrate that their coupled model improved the wave simulation, in comparison to a decoupled SWAN model.
In this research, a simplified but adequately accurate and efficient analytical method is proposed to estimate the effect of tidal currents on the wave power resource. Wave power, in general, is proportional to the wave group velocity and the wave height squared (see Eq. (1)); hence, WCI effects on both properties are included in the method. A limitation is that the method assumes waves are either following or opposing the currents. This assumption is valid in the majority of laboratory studies [12] and also applies in the field to many wave energy sites [13].
Section snippets
Theoretical background
Both wave height – which quantifies the magnitude of wave energy – and group velocity – which is the speed of wave energy transport – are modified by tidal currents. Here, we present a simple analytical method, based on the linear wave theory, for estimating these changes as a function of the current velocity, when currents and waves are aligned (opposing or following). We will only consider deep water waves (or nearly), for which linear theory is a reasonable approximation. We will also assume
Field data for validating the proposed method
The simple analytical method presented above is valid for any site where the assumptions made are realistic, i.e., linear deep water waves over a stationary current. As indicated, however, it is also hoped that the method would apply to waves that have already somewhat entered the intermediate water depth regime. This will be verified using field data.
In the following, we assess the performance of the simplified method for two sites on the UK shelf, in which wave data was collected using wave
Results
In Fig. 9, we computed the ratio of wave properties in the presence and absence of a tidal current, using the simplified method described in Section 2.2 and summarized in Table 2, for a range of wave periods T and current velocities u. This figure also demonstrates that using the complete equations (i.e. Section 2.2) does not lead to a significant difference. Results were calculated for a nominal 40 m water depth, assuming deep water conditions; however, using the complete equations, it can be
Discussion
Besides the assumptions introduced in Section 2.1, other considerations should be taken into account when applying the simplified method. The effect of tidal elevation variations was ignored, as it was previously shown (using coupled models), that this parameter has much less effect on wave power than currents [9]. Assuming linear wave theory also implies that the actual sea state is approximated by a superposition of harmonic waves, in which no sinks or sources of energy interact with the wave
Conclusions
We presented a simplified method, based on linear wave theory, which can be used to predict the effects of tidal currents on the wave power resource. The method demonstrates that one can expect a significant increase in wave height and power when currents are opposing waves (e.g., a 60% increase in wave height for a −2.0 m/s current and a 8 s wave period), and a decrease in these quantities, albeit smaller, when waves are following the currents (e.g., a 20% decrease in wave height for a + 2.0 m/s
Acknowledgements
Thanks to Cefas WaveNet for supplying the wave buoy data at Scarweather, and to Philippe Gleizon (University of the Highlands and Islands, Thurso) for providing wave buoy data at Pentland Firth. S.P. Neill acknowledges financial support provided by the Welsh Government and Higher Education Funding Council for Wales through Sêr Cymru National Research Network for Low Carbon Energy and the Environment.
References (40)
- et al.
Inter-annual and inter-seasonal variability of the orkney wave power resource
Appl. Energy
(2014) - et al.
Wave-current interaction within and outside the bottom boundary layer
Coast. Eng.
(1993) - et al.
Methods for medium-term prediction of the net sediment transport by waves and currents in complex coastal regions
Cont. Shelf Res.
(2009) - et al.
Improving the assessment of wave energy resources by means of coupled wave-ocean numerical modeling
Renew. Energy
(2013) - et al.
The role of tides in shelf-scale simulations of the wave energy resource
Renew. Energy
(2014) - et al.
Wave–current interaction effects on marine energy converters
Ocean Eng.
(2013) - et al.
Realistic wave conditions and their influence on quantifying the tidal stream energy resource
Appl. Energy
(2014) - et al.
The role of tidal asymmetry in characterizing the tidal energy resource of Orkney
Renew. Energy
(2014) - et al.
Development of a coupled ocean–atmosphere–wave–sediment transport (coawst) modeling system
Ocean. Model.
(2010) - et al.
The economic impacts of marine energy developments: a case study from scotland
Mar. Policy
(2014)
Wave power variability over the northwest European shelf seas
Appl. Energy
Some observations of wave–current interaction
Coast. Eng.
A numerical study of wave refraction in shallow tidal waters, Estuarine
Coast. Shelf Sci.
Uncertainty in wave energy resource assessment. part 2: variability and predictability
Renew. Energy
Quantifying the global wave power resource
Renew. Energy
Ocean Wave Energy Conversion
Wave energy utilization: a review of the technologies
Renew. Sustain. Energy Rev.
Atlas of UK Marine Renewable Energy Resources
Modeling the tide-induced modulation of wave height in the outer seine estuary
J. Coast. Res.
3D modelling in the Sado estuary using a new generic vertical discretization approach
Oceanol. Acta
Cited by (15)
A novel and simple passive absorption system for wave-current flumes
2023, Alexandria Engineering JournalA review of the state of research on wave-current interaction in nearshore areas
2022, Ocean EngineeringCitation Excerpt :Analysis of the wave frequency spectra indicated that the following (opposing) current led to a decreased (increased) significant wave height. More recently, Hashemi et al. (2016) determined changes in wave heights and wave lengths induced by the ambient current, based on the linear wave theory. Field data from the UK shelf and in the Bristol Channel were collected and used for validation.
Numerical study to estimate the wave energy under Wave-Current Interaction in the Qingdao coast, China
2017, Renewable EnergyCitation Excerpt :The currents can modify the shape and the spectra of waves [23], and thus the WCI should be taken into account when performing wave energy resources analysis and sites election work for deploying wave energy conversion devices. Benefiting from the increase of numerical models efficiency and computational capabilities, successful applications under WCI have been carried out in recent years [23–29]. Warner et al. [27] have found that the differences for significant wave heights in certain conditions increased by as much as 20% when a wave system meets an opposite current by utilizing a 3-D Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) system.
Modelling effects of tidal currents on waves at a tidal stream energy site
2017, Renewable EnergyCitation Excerpt :The present study extends these numerical investigations relying on a modified version of a phase-averaged spectral wave model (1) coupled with a tidal circulation model and (2) assessed against in-situ measurements of current-impacted waves parameters (wave height, period and direction) in the tidal stream site of the Fromveur Strait. Whereas a simplified analytical method, based on linear wave theory, has been recently proposed by Hashemi et al. [22] to estimate, with reduced computational costs, the effects of tidal currents on the wave power resource, this approach is not retained here as it only applies for colinearity situation between waves and currents neglecting further processes such as waves breaking and blocking by opposing currents [23,24]. As such situations are liable to occur in tidal stream sites [21], the present investigation is based on numerical wave modelling liable to encompass the processes of generation, dissipation and nonlinear wave-wave interactions from offshore opened ocean to coastal regions [25].