Page 58 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

50 Fundamentals of Ocean Renewable Energy

where h is water depth. The mean depth of the world’s oceans is around 4000 m,
and so c = 200 m/s. At the equator, the Earth turns at around 460 m/s. Therefore,
tidal waves cannot move as fast as the Earth spins.
The equilibrium tide does not account for continents, which hinder the
progress of the tidal wave. In addition, water that moves over a rotating Earth
is deflected by Coriolis forces, which arise as a result of the Earth’s spin (see
Section 3.6).
Wave speed is controlled by the local water depth (Eq. 3.2). For a typical
shelf sea water depth of h = 200 m, the tidal wave propagates at 44 m/s. Given
a tidal period T of 12.42 h (see Section 3.8), the wavelength L = cT is around
2000 km.

3.2 PROGRESSIVE WAVES
The time of high water (HW) at a particular location depends on how fast the
tidal wave can travel (Eq. 3.2), and so HW will not necessarily occur when
the Moon is directly overhead. Currents in a progressive wave flow with the
wave under the crest, and in the opposite direction under the trough (Fig. 3.5).
Maximum currents in a progressive wave correspond with HW and low water
(LW). The maximum current speed V beneath the wave is given by shallow
water wave theory as

R g
V = (3.3)
2 h
where R = 2a is the tidal range.

FIG. 3.5 An idealized progressive tidal wave. Peak (positive, or flood) currents occur under the
crest (HW), and peak (negative, or ebb) currents under the trough (LW).