Page 62 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

54 Fundamentals of Ocean Renewable Energy

FIG. 3.9 Standing wave plotted along a channel at the time of HW+T/4 at the coast. In this
case, zero elevations occur along the channel, and there are maximum (enhanced) currents at the
nodes.

considered as the right-hand portion of Fig. 3.7, between the node at L/4 and
the coast. The currents at the entrance to the channel (L/4) could lead to large
changes in water surface elevation at the head of the channel. The natural period
for such a forced oscillation is
4 × channel length L
√ = √ (3.7)
gh gh
For the M2 tidal constituent, which has a period of 12.42 h, if we assume a
water depth of 50 m

L = T gh (3.8)
and L ≈ 1000 km, and so the length of the channel, which would be at
quarter wavelength resonance, is around 250 km. This is approximately the
distance between the southern entrance to the Irish Sea and the coastline in the
northeastern part of the Irish Sea (Fig. 3.6), and so the Irish Sea can be said to
be close to resonance with the M2 tide.
In nature, forced resonant oscillations cannot grow indefinitely because
energy losses due to friction increase more rapidly than the amplitudes of the
oscillations. Regions of the world which experience resonance, and so are
celebrated for their very large tidal ranges, are the Bay of Fundy (Canada)
(spring tidal range of almost 15 m in the Minas Basin) and the Bristol Channel
(UK) (spring tidal range of 13 m at Avonmouth).