Limits to Tidal Power

Ocean tides have been proposed as a source of renewable energy, though the maximum available power may be shown to be only a fraction of the present dissipation rate of 3.5 TW, which is small compared with global insolation (nearly 105 TW), wind dissipation (103 TW), and even human power usage of 15 TW. Nonetheless, tidal power could be a useful contributor in some locations. Traditional use of tidal power, involving the trapping of water behind a barrage at high tide, can produce an average power proportional to the area of the headpond and the square of the tidal range; the power density is approximately 6 W per square meter for a tidal range of 10 m. Capital costs and fears of environmental damage have put barrage schemes in disfavor, with interest turning to the exploitation of strong tidal currents, using turbines in a manner similar to wind turbines. There is a limit to the available power, however, as adding turbines reduces the flow, ultimately reducing the power. For sinusoidal forcing of flow in a channel connecting two large open basins, the maximum available power may be shown to be given approximately by 0.2ρ g a Q_max, where ρ is the water density, g gravity, a the amplitude of the tidal sea level difference along the channel, and Q_max is the maximum volume flux in the natural state. The same formula applies if the channel is the entrance to a semi-enclosed basin, with a now the amplitude of the external tide. A flow reduction of approximately 40% is typically associated with the maximum power extraction. The power would be reduced if only smaller environmental changes are acceptable, and reduced further by drag on supporting structures, dissipation in turbine wakes, and internal inefficiencies. It can be suggested that the best use of strong, cold, tidal currents is to provide cooling water for nuclear reactors.