travelling waves in water of depth d that is shallow compared to the wave-
length of the waves (figure G.2). The power per unit length of wavecrest
of shallow-water tidal waves is



Table G.3 shows the power per unit length of wave crest for some plausible
figures. If d = 100 m, and h = 1 or 2 m, the power per unit length of wave
crest is 150 kW/m or 600 kW/m respectively. These figures are impressive
compared with the raw power per unit length of ordinary Atlantic deep-

water waves, 40 kW/m (Chapter F). Atlantic waves and the Atlantic tide
have similar vertical amplitudes (about 1 m), but the raw power in tides is
roughly 10 times bigger than that of ordinary wind-driven waves.

Taylor (1920) worked out a more detailed model of tidal power that
includes important details such as the Coriolis effect (the effect produced
by the earth’s daily rotation), the existence of tidal waves travelling in the
opposite direction, and the direct effect of the moon on the energy flow in
the Irish Sea. Since then, experimental measurements and computer models
have verified and extended Taylor’s analysis. Flather (1976) built a
detailed numerical model of the lunar tide, chopping the continental shelf
around the British Isles into roughly 1000 square cells. Flather estimated
that the total average power entering this region is 215 GW. According
to his model, 180 GW enters the gap between France and Ireland. From
Northern Ireland round to Shetland, the incoming power is 49 GW. Be-
tween Shetland and Norway there is a net loss of 5 GW. As shown in
figure G.4, Cartwright et al. (1980) found experimentally that the average
power transmission was 60 GW between Malin Head (Ireland) and Florø
(Norway) and 190 GW between Valentia (Ireland) and the Brittany coast
near Ouessant. The power entering the Irish Sea was found to be 45 GW,
and entering the North Sea via the Dover Straits, 16.7 GW.

The power of tidal waves

This section, which can safely be skipped, provides more details behind
the formula for tidal power used in the previous section. I’m going to

Figure G.2. A shallow-water wave. Just like a deep-water wave, the wave has energy in two forms: potential energy associated with raising water out of the light-shaded troughs into the heavy-shaded crests; and kinetic energy of all the water moving around as indicated by the small arrows. The speed of the wave, travelling from left to right, is indicated by the much bigger arrow at the top. For tidal waves, a typical depth might be 100 m, the crest velocity 30 m/s, the vertical amplitude at the surface 1 or 2 m, and the water velocity amplitude 0.3 or 0.6 m/s.
0.9 125
1.0 155
1.2 220
1.5 345
1.75 470
2.0 600
2.25 780
Table G.3. Power fluxes (power per unit length of wave crest) for depth d = 100 m.