Mathematical Problems of Tidal Energy

1. Tidal energy. Recent studies of alternative energy sources have embraced a number of "exotic" forms such as solar, wind, geothermal or tidal energy. Here we shall examine recent developments in the mathematical understanding of tides and tidal power, with particular reference to the Bay of Fundy in eastern Canada which has the highest tides and may be the test site for further development of this mode of electrical energy production. From the observed increase in length of the day [21] and the observed lunar acceleration, the total rate of all tidal energy dissipation is known to be about 3 x 10 ergs per second—a rate comparable to mankind's present consumption of energy. Much of this energy is dissipated in certain oceanic high tide regions where shallow continental shelf areas create large amplitudes by resonance, shallowing and convergence, Thus the English Channel and Irish Sea absorb perhaps 4% of the overall total while the Bay of Fundy and Gulf of Maine account for about 1 %, an energy flow equal to the present capacity of the Canadian electricity network. Recent engineering studies have shown [2] that recommended sites at Economy Point, Nova Scotia, and Cape Maringouin, New Brunswick, would be feasible but probably not yet economical. Tidal energy is renewable, but not conservable, predictable but intermittent, and large yet limited (at these sites perhaps 8,000 megawatts capacity could be installed). An interesting recent suggestion for excess power at peak generating periods is compressed air storage in salt caverns, with subsequent coal burning. The applied mathematical problems discussed here are of two types. First is the description and calculation of oceanic and estuarial tidal wave motion and the modifications that would be induced by the construction of a tidal barrier with