Page 68 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

60 Fundamentals of Ocean Renewable Energy

diurnal inequalities (due to O1 and K1, in combination with the semidiurnal
constituents).
Although the previous example is for tidal elevations, a similar procedure
can be applied to predict tidal currents, and by using tidal ellipses, which will
be explained later in this chapter. The main difference between predictions of
elevations and currents is that water current measurements that are suitable
for analysis are more difficult to obtain. For tidal energy projects, these tend
to be obtained (due to cost) at scoping or initial planning stage via numerical
simulations (Chapter 8), and via ADCP deployments at later stages of project
development (Chapter 7).
Tidal analysis can be conveniently performed by computer software, and one
of the most popular choices for oceanographers and tidal energy practitioners is
T_TIDE, which runs in the Matlab environment [3]. Although it is tempting
to treat T_TIDE as a black box, it is useful to understand the choice of
constituents used in the analysis. Critical to this is the Rayleigh criterion, which
states that only constituents separated by at least a complete period from their
neighbouring constituents should be included in the analysis [4]. For example,
to analyse a time series for M2 and S2 requires a minimum record length of

360/(30.0 − 28.98) h = 14.77 days (3.19)
(speeds of the constituents taken from Table 3.1). An additional useful func-
tionality of T_TIDE is that it estimates the error for each of the analysed
constituents.

3.9 COMPOUND TIDES
In Section 3.1, we discussed tide generating forces within the context of
a simplified Earth-Moon system. However, the effects of the Sun are also
important. Although the Sun is considerably further away from the Earth than
the Moon, its mass is 27 million times the mass of the Moon. As a result,
the influence of the Sun on the tides is significant, but is around half of the
Moon’s influence, and it is manifested through the principal semidiurnal solar
constituent, S2 which, because time on Earth is measured relative to the Sun,
has a period of exactly 12 h. Relative positions of the Sun, Moon, and Earth
are shown in Fig. 3.13 for two scenarios. When the Sun and the Moon are
in line with the Earth, during either a full Moon or new Moon (Fig. 3.13A),
the combined tide generating forces are at their greatest effect, and this leads
to spring tides (mean high water spring (MHWS) and mean low water spring
(MLWS), as shown on Fig. 3.14). By contrast, when the Sun and Moon are
perpendicular to each other in relation to the Earth (Fig. 3.13B), they have their
least effect. This occurs at the first or third quarter of the Moon’s phase, and
leads to neap tides, associated with mean high water neap (MHWN) and mean
low water neap (MLWN), again shown in Fig. 3.14. The combination of M2 and
S2 tidal constituents is known as a compound tide, and the combined signal (in
addition to the diurnal constituents K1 and O1) can be seen in Fig. 3.12, with