the power of the wave will remain constant. This means √dh2 is a constant,
so we deduce that the height of the tide scales with depth as h ≅ 1/d1/4.
This is a crude model. One neglected detail is the Coriolis effect. The
Coriolis force causes tidal crests and troughs to tend to drive on the right –
for example, going up the English Channel, the high tides are higher and
the low tides are lower on the French side of the channel. By neglecting
this effect I may have introduced some error into the estimates.
Imagine sticking underwater windmills on the sea-bed. The flow of water
will turn the windmills. Because the density of water is roughly 1000 times
that of air, the power of water flow is 1000 times greater than the power of
wind at the same speed.
What power could tidal stream farms extract? It depends crucially
on whether or not we can add up the power contributions of tidefarms on
adjacent pieces of sea-floor. For wind, this additivity assumption is believed
to work fine: as long as the wind turbines are spaced a standard distance
apart from each other, the total power delivered by 10 adjacent wind farms
is the sum of the powers that each would deliver if it were alone.
Does the same go for tide farms? Or do underwater windmills interfere
with each other’s power extraction in a different way? I don’t think
the answer to this question is known in general. We can name two alternative
assumptions, however, and identify cartoon situations in which each
assumption seems valid. The “tide is like wind” assumption says that you
can put tide-turbines all over the sea-bed, spaced about 5 diameters apart
from each other, and they won’t interfere with each other, no matter how
much of the sea-bed you cover with such tide farms.
The “you can have only one row” assumption, in contrast, asserts that
the maximum power extractable in a region is the power that would be
delivered by a single row of turbines facing the flow. A situation where
this assumption is correct is the special case of a hydroelectric dam: if the
water from the dam passes through a single well-designed turbine, there’s
no point putting any more turbines behind that one. You can’t get 100