Earth Sciences and Ecology Question #372

Larry King, a 39 year old male from the Internet asks on April 20, 1998,

How can you measure the energy of an ocean wave? Is there a reasonably simple equation that describes the energy in water waves?

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The answer

Fred Dobson answered on April 20, 1998

You should realize all this was worked out in the 1800's by people like Lord Kelvin and Lord Rayleigh - we're dealing with good solid physics that has stood the tests of time. In deep water (wavelength > 4xdepth) a wave with trough-to-crest height H = 2A (A is called amplitude), the total energy of a wave per unit area of sea surface is (Rho g A^2) / 2, where Rho is the density of water (1,000 kilos/cubic meter), g is the acceleration due to gravity (about 9.8 meters/sec^2) and A^2 means "A squared". The area to use is simply the crest-to-crest distance (the wavelength) times the desired along-wave distance. The energy is equally divided between kinetic and potential energy. If you want to read lots and lots about waves, you should find Wind Waves: Their Generation and Propagation on the Ocean Surface by Blair Kinsman, Prentice-Hall 1965, 676 pp. It's a wonderful book - a lot of mathematics, but in between are the desired formulae.

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