Page 74 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

66 Fundamentals of Ocean Renewable Energy

Overtides and compound tides are the main causes of tidal asymmetry, and
their role in processes such as sediment transport and tidal energy conversion are
important in some regions [7–9]. It can easily be shown that tidal asymmetry is
controlled by the phase difference of semidiurnal and quarter-diurnal tidal con-
stituents. Therefore, tidal asymmetry can be described by comparing the phases
of M 2 and M 4 tidal constituents, as well as the ratio of M 4 /M 2 amplitudes.

3.11 CHARACTERIZING TIDES AT A SITE

3.11.1 Velocity Profile
The bottom boundary layer is defined as the region of flow in which the
dynamics are influenced by frictional effects due to the sea bed. In relatively
shallow waters, the boundary layer may occupy the entire water column, but in
deeper water it will occupy only the lower part of the water column. The way
in which the current increases with height above the sea bed is known as the
velocity profile. Many engineers adopt what is known as the one-seventh power
law to characterize the velocity profile
z

1/7
U z = U (3.27)
0.32h
where U is the depth-averaged current speed, z is the height above the sea bed,
h is the water depth, and 0.32 is the bed roughness chosen for this example
[10]. The resulting velocity profile (Fig. 3.19) demonstrates that, theoretically,
the current speed is zero at the sea bed, and increases with height above the sea
bed. In addition, shear (du/dz) is greater in the lower part of the water column.
Therefore, it is advantageous from both resource and design perspectives to
place the rotor as high in the water column as possible, subject to navigational
and economic constraints.

3.11.2 Power Density
Instantaneous ‘theoretical’ power density (per unit area) can be calculated as
P 1 3
= ρu (3.28)
A 2
where P is the power output in W, A is the swept area of the rotor, ρ is the
water density, and u is the depth-averaged current speed. Clearly, since power
output depends on the cube of current speed, a small increase in current speed
leads to a large increase in power output (Fig. 3.20). This is why developers
generally seek sites with high current speeds to maximize net power output. For
example, at a peak current speed of 1 m/s, net power output over a tidal cycle in
this example is <1 MWh. By increasing peak current speed to 3 m/s, net power
output increases to >23 MWh, that is over 20 times the power output! Eq. (3.28)
neglects device efficiency, and this is considered in detail in Section 3.13.