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Scottish Wave Energy Plans Move Forward
It's been a long time coming (2007, 2005, and 2002 respectively), but the project to harness wave energy off the Scots coast is finally coming together. Reader krou writes: "The BBC is reporting that ten sites on the seabed off Scotland in Pentland Firth and around Orkney have been leased to energy companies with the hopes of generating wave and tidal energy. 'Six sites have been allocated for wave energy developments potentially generating 600 megawatts of power and four for tidal projects, also generating 600 MW.' The leases were awarded to SSE Renewables Developments, Aquamarine Power, ScottishPower Renewables, E.ON, Pelamis Wave Power, OpenHydro Site Developments, and Marine Current Turbines. Scotland's First Minister Alex Salmond said that 'These waters have been described as the Saudi Arabia of marine power and the wave and tidal projects unveiled today — exceeding the initial 700MW target capacity — underline the rich natural resources of the waters off Scotland.'"
We sometimes forget just how heavy water is, or how much energy ocean waves carry.
Some time ago, I did some statistical analysis of wave heights in Scapa Flow, not far away from the site proposed here in northern Scottish waters. It has very steady, large swells.
Imagine a wave (or swell) of 10m peak height, extending 2 km across, and 50m front-to-back. That's a nice 0.3 * 10^6 kg of water ... move it forward at 30kph ... repeat every 10 or 20 seconds, and you've got 10^9 Joules/second, about 1GW. For the surface wave. (More energy is transferred more steadily by sub-surface currents.)
Lunar tidal flows are so much larger than these that the prospect of drawing enough energy from open waters to do anything to earth - moon movements seem to be off by many orders of magnitude.
Full disclosure: I used to be a pretty good physicist, but that was a long time ago.
You calculated the kinetic energy of a mass of water moving forward at 30kph. In a wave water is not moving forward at the wave speed, but rather gently in an elliptic trajectory. I gather you used 10m as amplitude and not crest to through height.
The energy flux of waves is given by the formula which you can find on this wikipedia page. A 20m (crest to through) wave with a period of 10s over a lenght of 50m gives you 20MW of wave energy. Still a lot, but almost 2 orders of magnitude less than 1GW.