Fourier Transforms in Oceans

I had trouble thinking of an application of Fourier Transforms.  At first, I thought I might look into acoustics and how sound waves propagate through the air, but I discarded that idea quickly because I didn't find it all that interesting.  It seemed too similar to the work we had done with light waves.  I sat for a while, trying to think of other things that came in waves.  Eventually (I'll spare you the details of my mind's twisty journey) I remembered myself sitting on the beach over winter break, looking up at the moon and hearing the tide come in.

I knew, then, that tides were the result of the gravitational pull from the moon and sun and the Earth's rotation.  I also knew that people had had the knowledge to predict the tides for years (though I had never given much though to how long this knowledge had been around).  Now that I know about Fourier transforms, I can (mostly) understand the theory behind tidal prediction.

Picture of ocean currents around the world from an Indiana University geology class site

http://www.indiana.edu/~geol105/1425chap4.htm

Just like the light waves in Young's double slit experiment, the currents in the above picture interfere with each other destructively and constructively.  When they interfere constructively, they create waves (or tsunamis when they interfere constructively and nature's in a bad mood).

The exact equations vary slightly from source to source, but the general idea is that tidal predictors do their work by relating Fourier transforms of the currents and average current information obtained from months or years of data collection.  In 1966, Munk and Cartwright developed the Response Method$^{_1}$ (which is the easiest method to explain) for predicting shallow water tides.  It uses the equation Z(f)=$\frac{G(f)}{H(f)}$ where G(f) and H(f) are Fourier transforms of the tide's potential and the data gathered, respectively and f is frequency.

$^{_1}$oceanworld.tamu.edu