Page 59 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Tidal Energy Chapter | 3 51

3.3 COTIDAL CHARTS
Cotidal charts of a region convey two important pieces of information: tidal
amplitude and tidal phase. Cotidal lines join locations that are in phase with one
another (e.g. HW would occur at the same time at these locations). Coamplitude
lines join locations that have equal tidal amplitudes. Cotidal and coamplitude
lines are shown on Fig. 3.6 for the M2 (principal semidiurnal lunar constituent)
over the northwest European shelf seas. The M2 tidal constituent has a period
of around 12.42 h (Section 3.8), and the cotidal contour interval on the chart is
30 degrees. Therefore, the contour interval can be converted into time as
30 degrees
× 12.42 ≈ 1h2min (3.4)
360 degrees
If we examine the Irish Sea in detail (Fig. 3.6) and assume that HW occurs
at midday (12:00) at the southern entrance to the Irish Sea, HW at Holyhead (90
degrees phase difference) would be at 15:00. The distance between these two
locations is 165 km. Therefore, the speed of the propagation of the tidal wave
can be calculated as
165 km
= 55 km/h = 15 m/s (3.5)
3h

For interest, and referring back to Eq. (3.2), the mean water depth h between
these two locations could be estimated as approximately 23 m.
Two additional points to note from the cotidal chart are that the tidal
amplitude in the northeastern part of the Irish Sea and in the Bristol Channel are
high, due to wave reflection (Section 3.4), and that there are various locations,
known as amphidromic points, where the tidal amplitude is theoretically zero,
due to the Earth’s rotation (Sections 3.6 and 3.7).

3.4 STANDING WAVES

In shelf seas, tides cannot propagate indefinitely as progressive waves, due to
reflection at coastal boundaries and at sudden changes in water depth. Incident
and reflected waves combine together to give the observed total tidal wave.
In the case of a wave propagating along a channel that is relatively long
in comparison to the tidal wavelength (Fig. 3.7), at a distance of 1/4ofa
wavelength from the coast, the crest of the incoming wave passes at the same
time as the trough of the reflected wave (and vice versa). The two waves
(incident and reflected) cancel at this point, known as a node, and so there
is no tide at this location. Nodes also occur at 3L/4, 5L/4, etc. Note that
since incoming and reflected waves combine, the amplitude a at the coast
becomes 2a.