the power of the wave will remain constant. This means √*d**h*^{2} is a constant,

so we deduce that the height of the tide scales with depth as *h* ≅ 1/*d*^{1/4}.

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