Reza Hashemi and Matt Lewis

Wave-Tide Interactions in Ocean Renewable

138 M.R. Hashemi and M. Lewis

therefore, wave-current interaction at marine energy sites needs to be considered for specific regions.

The effect of waves upon the tidal resource, and the effect of tides on the wave resource, needs to be quantified for accurate resource assessment and device design.

Wave power is proportional to the square of wave height, and tidal-stream power is proportional to the cube of current speed; therefore, small modulations due to wave-tide interaction could have a large effect on the marine renewable energy resource.

Furthermore, during an extreme event, renewable energy devices are likely to go into a shutdown mode to decrease the likelihood of damage; however the conditions for the threshold of device shutdown are unclear and the effect to electricity supply is unquantified.

As a first-order approximation, the wave conditions at potential tidal-stream energy sites, and the tidal conditions at potential wave energy sites are investi-gated on a global scale to show wave-tide interaction is an important process to consider in marine renewable energy development (see Fig.1). Tidal constituents were extracted from the FES2012 (Finite Element Solution) data-assimilated global tidal model (Carrère et al.2012) at 1/16^◦ resolution, with the peak tidal amplitude (associated with tidal elevation) and peak tidal current speeds assumed to be rep-resented by the sum of the four major tidal constituents that describe the majority of the diurnal and semidiurnal tidal movement around the globe (see Pugh 1996;

Robins et al.2015). Global mean daily significant wave heights for a typical year (2014) were extracted from the European Centre for Medium-Range Weather Fore-casts (ECMWF) ReAnalysis, ERA-interim product (Dee et al. 2011) at 3/4^◦ res-olution (Fig.1c). Interpolating ETOPO2 (Earth TOPOgraphy) bathymetric data at 1/30^◦resolution (see Marks and Smith2006), the ERA-interim wave climate and the FES2012 tidal climate data onto a common grid (the 1/16^◦ FES2012 grid), allows the wave and tidal conditions at potential marine energy sites around the world to be assessed (Fig.2). The daily mean wave height (averaged for 2014) is likely to be greater than 1 m for the majority of theoretical tidal-stream energy sites when resolved at 1/16^◦ (hence some grey shaded regions that represent unresolved sites;

see Fig.2), and for many potential tidal energy sites (especially second generation sites; Lewis et al.2015) having a yearly average daily wave height above 3 m (Fig.2a and b).

Using the global mean daily wave height (H, see Fig.1) and period (T), theo-retical wave energy sites are assumed to be represented by high daily mean wave power estimates, averaged for 2014, with the representative tidal conditions shown in Fig.2c and d, which reveal tidal currents>0.5 m/s and tidal range >2 m can be expected at potential wave energy sites around the globe.

Although many marine energy sites, such as the wave sheltered tidal-stream energy resource in Puget Sound USA, are unlikely to have significant wave-tide inter-action because of their locations, some potential tidal energy sites around the globe will experience significant wave exposure, and conversely may experience strong wave-tide interaction. Nevertheless, the analysis of Figs.1 and 2 cannot resolve processes below 1/16 spatial resolution (and wave analysis is for 1 year only and thus cannot resolve interannual variability). Hence, specific developments maybe in

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Fig. 1 The global distribution of the tide and wave energy resource (2014). a Peak tidal ampli-tude (associated with tidal elevation) and b peak current speed are represented by the sum of K1, O1, S2, and M2 constituents from the FES2012 database, and daily wave height c averaged from ERA-interim data for 2014. Acronyms FES (Finite Element Analysis); ERA (ECMWF ReAnalysis);

ECMWF European Centre for Medium-Range Weather Forecasts

140 M.R. Hashemi and M. Lewis

Fig. 2 The 2014 averaged daily wave height conditions at theoretical tidal range a and tidal-stream benergy sites around the globe, with the corresponding tidal conditions c and d at theoretical wave energy sites shown as the percentage of the global ocean area (resource distribution) based on Fig.1

regions of low wave-tide interaction, and yet in many parts of the world (as discussed previously) the influence of waves on tidal energy schemes, and the influence of tides on wave energy schemes, may need to be considered.

To further demonstrate the wave-current interaction problem, Fig.3shows that significant wave events were observed over a 5 month period at two UK poten-tial tidal-stream energy sites: the Crown Estates tidal energy demonstration zone in North West Anglesey (Site A, 172 days), and the Pentland Firth (Site B, 182 days).

Mean wave conditions during the observation period (see Fig.1) were 1.50 m and 7.5 s at Site A, and 1.07 m and 5.6 s at Site B. The largest waves of 6.6 m (11 s) and 5.45 m (8.7 s) were observed at Site A (Winter) and Site B (Summer) respectively, and the wave climate was demonstrated by the probability density (% of occurrence in 20 cm and 1 s bin sizes) shown in Fig.3. Therefore, challenges surrounding waves at tidal-stream energy sites are an important consideration for some regions of the world, and if the true global potential of tidal energy is to be realized then these challenges need to be considered in the design and maintenance of marine renew-able devices and associate resource assessment studies.

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Fig. 3 The observed wave climate at two potential tidal-stream energy sites in the UK; the Crown Estates NorthWest Anglesey Demonstration Zone (Site A), and the Pentland Firth (Site B)

For resource characterizations, in many modeling studies, the interactions of waves and tides have been ignored by assuming that they are not be significant (e.g., Smith et al.2013; ABPmer2008; Neill et al.2014; Draper et al.2014) even though this assumption may not be valid in many of the regions (e.g., González-Santamaría et al.2010; Saruwatari et al.2013). Further, it is possible to simulate the effect of tides on a wave energy resource or vice versa by employing coupled model-ing systems. However, these models are computationally more expensive, and more challenging to develop and validate. Therefore, it is helpful to understand wave-tide interaction processes, and the simple and basic methods that can quantify the importance of these processes, before developing complex numerical models. In observation-based data, which are collected to characterize the marine energy of a site, wave-tide interaction effects are inherently included. However, measurements usually take place during a particular period (e.g., certain wave conditions, facing a certain tidal current), and are usually carried out at specific locations. The con-cepts discussed in this chapter help understand and generalize measurement results for various locations and other time periods, which may involve different conditions.

142 M.R. Hashemi and M. Lewis

This chapter introduces the topic of wave-current interaction within the context of marine renewable energy resource characterization, summarizing current research and discussing simple and advanced techniques for assessing associated impacts.

The implications of wave-tide interaction on energy devices is another topic of inter-est, that needs to be discussed separately because the scale of the processes and tools, and concepts are different. A short discussion about this topic and some references are included.

Introduction to Wave-Tide Interaction

Tides and waves can be regarded as long and short waves that interact in multiple ways. Doppler shift is a clear example in which the frequency of waves changes by ambient current:

𝜔 = 𝜎 + ku (1)

where 𝜎 is intrinsic or relative wave frequency (observed in a coordinate system moving with the same velocity as the ambient current),𝜔 is the absolute wave fre-quency (observed in a fixed frame), u is the ambient current velocity, and k is the wave number. For wave energy development studies, a relevant question is whether the presence of tides and their effect on waves can be significant during various stages of a project such as site characterization, or evaluation of the performance of a wave energy device. In theory, wave energy propagates with group velocity which directly depend on water depth and ambient currents (Dalrymple and Dean1991):

C_g= 𝜎

k = 𝜔 −ku k {1

2(1 + 2kh

sinh 2kh)} (2)

where C_gis the group velocity, and h is the water depth; the angular frequency and wavenumber are related to water depth by the linear dispersion relationship,

𝜎² = (𝜔 − uk)²= gk tanh(kh) (3)

Because tides change water depth and generate currents, they can change the prop-agation of wave energy. Further, the magnitude of wave energy is proportional to the wave height squared, which also changes with ambient currents. For instance, currents opposing waves can cause a significant increase in wave height and lead to wave breaking or even complete blockage of wave energy propagation.

Similar issues may arise during tidal-stream project development. In general, waves interact with the shallow water bottom boundary layer, and enhance the bot-tom roughness. This process, particularly in shallow waters, leads to an increase in the bed shear stress, and consequently, the slowdown of tidal currents. Because tidal power is proportional to velocity cubed, this can have some impact on the tidal energy resource at a site (e.g., see Guillou et al.2016). Also, wave-induced momen-tum, caused by wave radiation stresses, can modify the dynamics of tides.

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In general, there are two questions about the implication of wave-tide interactions in marine renewable energy studies: When/where can these interactions be ignored?

If significant, how can wave-tide interaction effects be included in studies at a rea-sonable cost? Here, we focus more on site characterization, but the implications for device design could be also important (e.g., Gaurier et al.2013). We present/review an introduction to simple and advanced techniques for assessing the effects of wave-tide interactions in marine renewable energy studies.