## Power in the waves

The power of a harmonic wave, i.e. the energy flux per unit length of wave crest, passing through a plane perpendicular to the direction of propagation, is from (2.84)

P = pw g Uw a2/4 = Pw g2 T a2 /(8n) = pa g2 a2 /(4a). (3.28)

For the spectral distribution of energy given by the function F1 (section 3.3.1), each component must be multiplied by the group velocity d a (k)/d k. Taking a = (gk)1/2 for ocean gravity waves, the group velocity becomes g/(2a), and the power becomes

Based on observed energy spectra, F1r as a function of frequency or period T = 2n/CO, the power distribution [(3.29) before integration] and total power may be constructed. Figure 3.46 gives the power distribution at the North Atlantic station also considered in Fig. 3.44. Using data for an extended period, the average distribution (labelled "year") has been calculated and, taking out data for the periods December-February and June-August, the curves labelled "winter" and "summer" have been constructed (Mollison et al., 1976).

Figure 3.46 (left). Frequency distribution of wave power, based on one year of observations (full line) or summer or winter data only (dashed lines), for Station India (59°N, 19° W) in the North Atlantic. The yearly average power is 91 kW m-1 (based on Mollison et al., 1976).

Figure 3.47 (below). Annual average wave power (in kW m-1) for selected sites (based on United Kingdom Energy Technology Support Unit, 1976).

Figure 3.47 (below). Annual average wave power (in kW m-1) for selected sites (based on United Kingdom Energy Technology Support Unit, 1976).

Longitude X (deg)

Compared with Fig. 3.34, for example, it is seen that the seasonal variations in wave power at the open ocean site considered in Fig. 3.46 are quite substantial and equivalent to the seasonal variations in wind power at considerable height (maybe around 100 m, considering that the roughness length over the ocean is smaller than at the continental site considered in Fig. 3.36).

Figure 3.47 summarises some of the data available on the geographical distribution of wave power. The figures given are yearly mean power at a specific location, and most of the sites chosen are fairly near to a coast, although still in open ocean. The proximity of a shore is considered important in connection with the potential for energy extraction from wave motion. Whether such a condition will be maintained depends on the development of suitable transmission methods for long-range energy transfer (see Chapter 5).

Figure 3.48. Contours of estimated equal annual average wave power in the North Sea, adjacent straits and a part of the North Atlantic Ocean (unit: kW m-1) (based on United Kingdom Energy Technology Support Unit, 1976).

In Fig. 3.48 a more detailed map of wave power availability for the north European region is shown, based on the iso-power lines estimated in initial assessments of wave power in the United Kingdom, supplemented with estimates based on data for the waters surrounding Denmark. One might note the rapid decrease in power when passing the Hebrides in approaching the Scot tish coast from the Atlantic and also when moving southwards through the North Sea.

The variability of wave power may be described in terms similar to those used for wind energy. Figure 3.49 shows the power duration curves for Station India in the North Atlantic, based on all year or the summer or winter periods only, as in Fig. 3.46. Again, the occurrence of periods of low and high power depends markedly on seasonal changes.

Figure 3.49. Time duration curves for wave power at Station India (59°N, 19°W) in the North Atlantic for the whole year (solid line) or only summer or winter (dashed lines) (based on Mollison et al., 1976).

### Waves in a climatic context

As in the case of wind energy, little is known about the possible impact of large-scale energy extraction from wave power. One may argue that the total amount of energy involved is so small compared to the energy exchanged by atmospheric processes that any climatic consequence is unlikely. However, the exchange of latent and sensible heat, as well as matter, between the ocean and the atmosphere may, to a large extent, depend on the presence of waves. In particular, the rates of transfer may be high in the presence of breaking waves, and the extraction of energy from the wave motion may prevent the waves from developing the wave profile to the point of breaking. Thus, a study of the environmental implications of wave energy utilisation, which seems to lend itself very naturally to computer simulation techniques, should be undertaken in connection with proposed energy extraction schemes. As suggested in previous sections, this is likely to be required for any large-scale use of renewable energy, despite the intuitive feeling that such energy sources are "non-polluting". Yet the limited evidence available, mostly deriving from analogies to natural processes, does suggest that the results of more detailed analyses will be that renewable energy flows and stores can be utilised in quantities ex ceeding present technological capability, without worry about environmental or general climatic disturbances.