Tidal Current Energy

118 A. Owen
pressure head and friction. The bottom friction or drag force, for a channel of
length L and width W , is given by:
Drag � CDLWρU2 where C D is the dimensionless drag coefficient, typically 0.002 at 1 m above the
seabed [5] , ρ is the density of sea water and U is the freestream velocity. The
force applied by the pressure head ( F P ) for a channel of width W and depth z is
given by:
F � ρghWz P
where h represents the head difference across the channel. Equating the two
forces given by Equations (2) and (3), and solving for U :
U �
zgh
C L
If h is found from the tide heights at each end of the channel, then the flow
velocity U can be found, after allowing sufficient time for the flow to develop.
However, this is a very simplistic analysis, and realistic modelling requires
much greater detail and substantial computing power [6] .
Tidal currents in coastal locations exhibit a significant friction loss at the seabed,
and thus have a vertical velocity profile which can be simply modelled
using a 1/7th power law approximation.
The interaction of tidal currents with the seabed produces a boundary layer
in which energy is lost to friction forces [7] . The earth, rotating once every sidereal
day, attempts to drag the lunar-induced bulges around with it, whilst the
moon’s gravitational effects tend to hold them in place. The interaction of the
water with the seabed induces turbulent eddies of decreasing scale that eventually
dissipate as a small quantity of heat. Consequently, the earth’s angular
momentum is decreased by the tidal friction induced between the water and the
seabed, particularly in the shallower seas. The retardation thus applied increases
the day length by 1 second every 41 000 years. It is therefore considered that,
since the energy that a tidal current energy device will extract is presently
largely dissipated as heat into the seabed, even the installation of thousands of
units will not have any measurable effect on the earth’s rotation.
2.9 . Wave action
Submerged tidal turbines will not generally be concerned with small-amplitude,
locally generated waves, but some accounting is necessary for relatively large
swell waves. The wave speed ( c ) in any water depth is given by [8] :
c �
D
g z
λ 2π
tanh
2π
λ
⎛ ⎞
⎜
⎝⎜
⎠⎟
(2)
(3)
(4)
(5)